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1999-12-11 03:00:00
2025-07-19 00:40:46
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A380404
Number of prime powers that do not exceed the primorial number A002110(n).
[ "0", "1", "4", "16", "60", "377", "3323", "42518", "646580", "12285485", "300378113", "8028681592", "259488951722", "9414917934636", "362597756958862", "15397728568256861", "742238179325555125", "40068968503380861518", "2251262473065725514585", "139566579946046888545036" ]
[ "nonn", "hard", "more" ]
10
0
3
[ "A000849", "A002110", "A182908", "A246655", "A380402", "A380404" ]
null
Michael De Vlieger, Jan 24 2025
2025-03-31T23:09:37
oeisdata/seq/A380/A380404.seq
241722484f10fd4dd4776eb5dac57740
A380405
Squares k such that there are no primes between k and the nearest cube that is not k.
[ "9", "25", "121", "32761", "79524", "97344" ]
[ "nonn", "hard", "more" ]
41
1
1
[ "A053706", "A078933", "A380405", "A380521", "A380522", "A380523" ]
null
Zhining Yang, Jan 26 2025
2025-01-28T13:56:30
oeisdata/seq/A380/A380405.seq
3f08c912e572ef9861b301e8f5d951f6
A380406
E.g.f. satisfies A(x) = exp( 2 * x * exp(x) * A(x)^(1/2) ).
[ "1", "2", "12", "104", "1232", "18592", "342208", "7451264", "187631872", "5369721344", "172255038464", "6125052946432", "239195824279552", "10179739052908544", "469024768235192320", "23263095316577681408", "1235978286454556131328", "70040404736026578386944", "4217180561907991530176512" ]
[ "nonn" ]
13
0
2
[ "A273953", "A273954", "A357247", "A360473", "A380406", "A380407" ]
null
Seiichi Manyama, Jan 23 2025
2025-02-16T08:34:07
oeisdata/seq/A380/A380406.seq
13326da690d44799539394610492209f
A380407
E.g.f. satisfies A(x) = exp( 3 * x * exp(x) * A(x)^(1/3) ).
[ "1", "3", "21", "207", "2697", "43803", "854685", "19512615", "510977937", "15112457523", "498560461989", "18160560320895", "724240913035545", "31394996915447883", "1470245245400432685", "73987438021589516247", "3982389565847576723745", "228331703268783136636515", "13894569264190369648271157" ]
[ "nonn" ]
16
0
2
[ "A273954", "A357247", "A380406", "A380407" ]
null
Seiichi Manyama, Jan 23 2025
2025-06-14T10:19:15
oeisdata/seq/A380/A380407.seq
39ad3e8d081c87f22c53bc03b057d531
A380408
a(n) = Sum_{k>=0} floor(n/(2k)!).
[ "0", "1", "3", "4", "6", "7", "9", "10", "12", "13", "15", "16", "18", "19", "21", "22", "24", "25", "27", "28", "30", "31", "33", "34", "37", "38", "40", "41", "43", "44", "46", "47", "49", "50", "52", "53", "55", "56", "58", "59", "61", "62", "64", "65", "67", "68", "70", "71", "74", "75", "77", "78", "80", "81", "83", "84", "86", "87", "89", "90", "92", "93", "95", "96", "98", "99", "101", "102", "104", "105", "107" ]
[ "nonn" ]
9
0
3
[ "A013936", "A013939", "A034968", "A038663", "A060832", "A380408" ]
null
Akiva Weinberger, Jan 23 2025
2025-02-05T22:24:22
oeisdata/seq/A380/A380408.seq
a95219787227919c3ad5ac45093dd7f0
A380409
Product of prime indices plus sum of prime factors.
[ "1", "3", "5", "5", "8", "7", "11", "7", "10", "10", "16", "9", "19", "13", "14", "9", "24", "12", "27", "12", "18", "18", "32", "11", "19", "21", "17", "15", "39", "16", "42", "11", "24", "26", "24", "14", "49", "29", "28", "14", "54", "20", "57", "20", "23", "34", "62", "13", "30", "21", "34", "23", "69", "19", "31", "17", "38", "41", "76", "18", "79", "44", "29", "13", "36", "26", "86" ]
[ "nonn" ]
5
1
2
[ "A000027", "A000040", "A000720", "A001222", "A001223", "A001414", "A003963", "A027746", "A055396", "A056239", "A061395", "A075254", "A075255", "A112798", "A175508", "A178503", "A319000", "A325032", "A325033", "A325034", "A325035", "A325036", "A325040", "A331384", "A379681", "A379682", "A380220", "A380344", "A380345", "A380409", "A380410" ]
null
Gus Wiseman, Jan 25 2025
2025-01-26T09:12:52
oeisdata/seq/A380/A380409.seq
412dd773bb6c492b2154011a6e1b25f6
A380410
Numbers with greater product of prime indices than sum of prime factors.
[ "1", "45", "49", "63", "75", "77", "81", "91", "99", "105", "117", "119", "121", "125", "126", "133", "135", "143", "147", "150", "153", "161", "162", "165", "169", "171", "175", "182", "187", "189", "195", "198", "203", "207", "209", "210", "217", "221", "225", "231", "234", "238", "242", "243", "245", "247", "250", "253", "255", "259", "261", "266", "270", "273" ]
[ "nonn" ]
5
1
2
[ "A000027", "A000040", "A000720", "A001222", "A001223", "A001414", "A002808", "A003963", "A027746", "A055396", "A056239", "A061395", "A075254", "A075255", "A112798", "A175508", "A178503", "A244623", "A301987", "A319000", "A325036", "A325037", "A325038", "A325040", "A325041", "A325044", "A331383", "A331384", "A379681", "A379682", "A380220", "A380344", "A380345", "A380409", "A380410", "A380411" ]
null
Gus Wiseman, Jan 25 2025
2025-01-26T09:12:28
oeisdata/seq/A380/A380410.seq
e2c167c3b9b20e4910901a4d7e4c414a
A380411
Number of integer partitions of n such that the product of parts is greater than the sum of primes indexed by the parts.
[ "1", "0", "0", "0", "0", "0", "0", "1", "4", "8", "14", "23", "39", "58", "85", "121", "168", "228", "308", "404", "533", "691", "892", "1136", "1449", "1820", "2291", "2857", "3553", "4387", "5418", "6646", "8144", "9931", "12086", "14649", "17733", "21379", "25747", "30905", "37049", "44282", "52863", "62936", "74841", "88792", "105202", "124387" ]
[ "nonn" ]
9
0
9
[ "A000009", "A000040", "A000041", "A001055", "A001223", "A001414", "A003963", "A025147", "A057567", "A057568", "A096276", "A111133", "A114324", "A175508", "A301987", "A318029", "A318950", "A319000", "A319005", "A319916", "A325037", "A325038", "A325044", "A326149", "A326152", "A326155", "A330954", "A331383", "A331384", "A379319", "A379320", "A379666", "A379720", "A379721", "A379722", "A379733", "A379734", "A379736", "A380217", "A380218", "A380219", "A380344", "A380410", "A380411" ]
null
Gus Wiseman, Jan 26 2025
2025-01-29T13:08:44
oeisdata/seq/A380/A380411.seq
7223c9ad5348d084da3937c6396062b1
A380412
First term of the n-th differences of the strict partition numbers. Inverse zero-based binomial transform of A000009.
[ "1", "0", "0", "1", "-3", "7", "-14", "25", "-41", "64", "-100", "165", "-294", "550", "-1023", "1795", "-2823", "3658", "-2882", "-2873", "20435", "-62185", "148863", "-314008", "613957", "-1155794", "2175823", "-4244026", "8753538", "-19006490", "42471787", "-95234575", "210395407", "-453413866", "949508390", "-1931939460" ]
[ "sign" ]
6
0
5
[ "A000009", "A000041", "A007442", "A008284", "A087897", "A129519", "A175804", "A218482", "A266232", "A281425", "A293467", "A320590", "A320591", "A377285", "A378622", "A378970", "A378972", "A380412" ]
null
Gus Wiseman, Feb 03 2025
2025-02-03T19:55:42
oeisdata/seq/A380/A380412.seq
4f8f0e2a376d8e752a53a1bac07bf2e4
A380413
Terms appearing twice in A378086 (number of nonsquarefree numbers < prime(n)).
[ "0", "1", "11", "14", "39", "53", "109", "179", "222", "240", "251", "319", "337", "481", "505", "508", "578", "664", "674", "738", "818", "835", "877", "905", "933", "1041", "1069", "1098", "1325", "1352", "1392", "1535", "1539", "1567", "1652", "1663", "1732", "1817", "1849", "1960", "2134", "2148", "2158", "2220", "2387", "2428", "2457", "2622", "2625" ]
[ "nonn" ]
5
1
3
[ "A000040", "A001223", "A005117", "A013929", "A036263", "A057627", "A061398", "A061399", "A065890", "A068360", "A068361", "A070321", "A071403", "A072284", "A076259", "A078147", "A112925", "A112926", "A120327", "A224363", "A337030", "A373198", "A376593", "A377783", "A378032", "A378033", "A378034", "A378036", "A378040", "A378082", "A378084", "A378086", "A380413" ]
null
Gus Wiseman, Feb 06 2025
2025-02-07T21:32:07
oeisdata/seq/A380/A380413.seq
a07385e24552ea9f49d155da3e038d30
A380414
a(n) = phi(2 + phi(3 + phi(4 + ... + phi(A246655(n))))), where phi is Euler's totient function (A000010).
[ "1", "2", "2", "4", "4", "4", "4", "4", "4", "4", "4", "4", "6", "8", "6", "4", "8", "8", "4", "8", "4", "4", "4", "4", "8", "4", "4", "6", "4", "4", "4", "4", "4", "4", "4", "4", "6", "4", "4", "4", "4", "4", "8", "4", "4", "4", "6", "4", "8", "8", "4", "4", "8", "4", "8", "8", "4", "4", "8", "4", "4", "4", "4", "4", "4", "8", "6", "4", "8", "4", "4", "8", "4", "8", "8", "4", "4", "8", "4", "4", "6", "4", "4", "8", "4", "4", "4", "4", "4", "8" ]
[ "nonn" ]
11
1
2
[ "A000010", "A246655", "A380340", "A380341", "A380342", "A380354", "A380414", "A380415" ]
null
Paolo Xausa, Jan 24 2025
2025-01-25T12:50:05
oeisdata/seq/A380/A380414.seq
e4bf3e316f616826941a68a33ccfd2e7
A380415
a(n) = phi(1 + phi(3 + phi(5 + ... + phi(2*n-1)))), where phi is Euler's totient function (A000010).
[ "1", "2", "6", "12", "18", "22", "42", "42", "72", "20", "48", "18", "12", "108", "20", "42", "20", "42", "20", "36", "42", "42", "36", "36", "36", "42", "20", "42", "42", "36", "36", "42", "20", "48", "48", "18", "36", "36", "36", "36", "48", "48", "20", "48", "48", "36", "20", "48", "96", "20", "96", "36", "20", "20", "42", "36", "36", "20", "36", "36", "36", "20", "20", "36", "36", "20" ]
[ "nonn" ]
16
1
2
[ "A000010", "A005408", "A380340", "A380341", "A380342", "A380414", "A380415" ]
null
Paolo Xausa, Jan 24 2025
2025-01-26T02:46:34
oeisdata/seq/A380/A380415.seq
4ad0542a15a0c0f2bf9b3a28104ba1a5
A380416
Number of corona for a diamond of edge n with diamonds of side 1.
[ "18", "83", "258", "627", "1298", "2403", "4098", "6563", "10002" ]
[ "nonn", "more" ]
17
0
1
[ "A000583", "A004767", "A016754", "A089207", "A380346", "A380416" ]
null
Craig Knecht, Jan 24 2025
2025-04-29T04:44:50
oeisdata/seq/A380/A380416.seq
08af3553842bb491fd359920bd0b8957
A380417
Split A377091 into sublists consisting of runs of terms with the same sign. Then a(n) = 1 if terms (in absolute value) in the n-th sublist form an arithmetic progression with common difference 1, 0 otherwise.
[ "1", "1", "0", "1", "0", "1", "0", "0", "1", "0", "1", "0", "1", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "1" ]
[ "nonn" ]
22
1
null
[ "A377091", "A379882", "A380417", "A380418", "A380419", "A380420", "A380510" ]
null
Paolo Xausa, Jan 24 2025
2025-01-27T06:22:46
oeisdata/seq/A380/A380417.seq
e2cb55cb12c8a02cea4141481b445e34
A380418
Split A377091 into sublists consisting of runs of terms with the same sign. Then a(n) = 1 if terms (in absolute value) in the n-th sublist form an arithmetic progression with common difference -1, 0 otherwise.
[ "1", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0" ]
[ "nonn" ]
21
1
null
[ "A377091", "A379882", "A380417", "A380418", "A380419", "A380422", "A380510" ]
null
Paolo Xausa, Jan 24 2025
2025-01-27T06:22:49
oeisdata/seq/A380/A380418.seq
69399ce9024f1affa573474e8de55db7
A380419
Split A377091 into sublists consisting of runs of terms with the same sign. Then a(n) = 1 if terms in the n-th sublist form an arithmetic progression with common difference 1 or -1, 0 otherwise.
[ "1", "1", "1", "1", "1", "1", "0", "0", "1", "0", "1", "0", "1", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "1", "1", "0", "0", "1", "0", "1" ]
[ "nonn" ]
15
1
null
[ "A377091", "A379882", "A380417", "A380418", "A380419", "A380423", "A380510" ]
null
Paolo Xausa, Jan 24 2025
2025-01-27T06:22:26
oeisdata/seq/A380/A380419.seq
ca5e057a3c0d762bd0383f19fc179e28
A380420
Positions of ones in A380417.
[ "1", "2", "4", "6", "9", "11", "13", "16", "18", "20", "22", "25", "27", "29", "31", "33", "36", "38", "40", "42", "65", "67", "74", "82", "85", "88", "90", "92", "97", "100", "103", "107", "110", "112", "114", "119", "121", "123", "126", "128", "130", "132", "135", "137", "139", "141", "143", "146", "148", "150", "153", "155", "157", "159", "162", "164", "166", "170", "173", "175" ]
[ "nonn" ]
7
1
2
[ "A377091", "A379882", "A380417", "A380420", "A380422", "A380423", "A380503" ]
null
Paolo Xausa, Jan 25 2025
2025-01-26T20:38:59
oeisdata/seq/A380/A380420.seq
2260b622a2a4054c0e5c8c25422b98c5
A380421
a(n) is the inverse of 2^3 modulo prime(n).
[ "2", "2", "1", "7", "5", "15", "12", "3", "11", "4", "14", "36", "27", "6", "20", "37", "23", "42", "9", "64", "10", "52", "78", "85", "38", "13", "67", "41", "99", "16", "82", "120", "87", "56", "19", "59", "102", "21", "65", "112", "68", "24", "169", "74", "25", "132", "28", "142", "86", "204", "30", "211", "157", "225", "33", "101", "34", "104", "246", "177", "110", "192", "39", "274" ]
[ "nonn", "look" ]
32
2
1
[ "A006254", "A292411", "A380421" ]
null
R. J. Cintra, Jan 25 2025
2025-02-24T22:44:40
oeisdata/seq/A380/A380421.seq
c73dee07ae2f4c6b0ad25e9f266854db
A380422
Positions of ones in A380418.
[ "1", "3", "5", "60", "63", "69", "80", "84", "102", "106", "117", "189", "193", "204", "210", "231", "237", "241", "249", "252", "258", "277", "281", "292", "301", "400", "432", "459", "464", "470", "476", "484", "487", "503", "507", "512", "516", "536", "540", "551", "560", "578", "582", "592", "713", "718", "722", "751", "769", "773", "782", "785", "795", "799", "803" ]
[ "nonn" ]
9
1
2
[ "A377091", "A379882", "A380418", "A380420", "A380422", "A380423", "A380504" ]
null
Paolo Xausa, Jan 25 2025
2025-01-26T20:39:22
oeisdata/seq/A380/A380422.seq
371803d3032dce279fc2359425f795b4
A380423
Positions of ones in A380419.
[ "1", "2", "3", "4", "5", "6", "9", "11", "13", "16", "18", "20", "22", "25", "27", "29", "31", "33", "36", "38", "40", "42", "60", "63", "65", "67", "69", "74", "80", "82", "84", "85", "88", "90", "92", "97", "100", "102", "103", "106", "107", "110", "112", "114", "117", "119", "121", "123", "126", "128", "130", "132", "135", "137", "139", "141", "143", "146", "148", "150", "153" ]
[ "nonn" ]
7
1
2
[ "A377091", "A379882", "A380419", "A380420", "A380422", "A380423", "A380505" ]
null
Paolo Xausa, Jan 25 2025
2025-01-26T20:39:49
oeisdata/seq/A380/A380423.seq
2e5c3038b33291b826d0e4e7e1cdb09d
A380424
Decimal expansion of zeta(2,1,-4) = Sum_{i>=3} Sum_{j=1..i-1} Sum_{k=1..j-1} (-1)^k/(i^2*j*k^4) (negated).
[ "5", "3", "7", "2", "9", "6", "4", "2", "6", "7", "1", "0", "1", "7", "0", "9", "3", "5", "9", "1", "3", "7", "5", "5", "3", "2", "7", "2", "1", "8", "4", "4", "9", "1", "0", "8", "1", "8", "0", "0", "9", "4", "2", "4", "3", "4", "6", "4", "5", "3", "5", "6", "7", "6", "0", "6", "6", "3", "9", "7", "5", "1", "6", "4", "1", "1", "6", "8", "9", "5", "5", "8", "3", "6", "0", "4", "8", "4", "1", "4", "3", "6", "6", "8", "7", "6", "3", "1", "1", "8", "8", "5", "0", "8", "0", "8", "8", "8", "5", "6", "8", "2", "6", "6", "7" ]
[ "nonn", "cons" ]
17
0
1
[ "A076788", "A255685", "A379826", "A379827", "A379829", "A380424" ]
null
Artur Jasinski, Jan 24 2025
2025-03-31T23:09:45
oeisdata/seq/A380/A380424.seq
03bb94ff528f94f594c055ab6f37324e
A380425
E.g.f. A(x) satisfies A(x) = exp( 2 * x * A(x)^(1/2) * exp(x * A(x)^(1/2)) ).
[ "1", "2", "12", "116", "1592", "28472", "630028", "16649348", "512197456", "17993496176", "711065689364", "31231930472492", "1509776777566648", "79670350504209896", "4557716010219325468", "280992142281969312548", "18574365176584473753248", "1310583528463442480750048", "98318677221689347734929956" ]
[ "nonn" ]
12
0
2
[ "A162695", "A360474", "A380406", "A380425", "A380426", "A380427" ]
null
Seiichi Manyama, Jan 24 2025
2025-01-24T11:59:53
oeisdata/seq/A380/A380425.seq
ad5c3062ee3066a697ba0ced96b1c546
A380426
E.g.f. A(x) satisfies A(x) = exp( 3 * x * A(x)^(1/3) * exp(x * A(x)^(1/3)) ).
[ "1", "3", "21", "225", "3309", "62223", "1430235", "38940681", "1227116409", "43970226651", "1766653847079", "78696970239165", "3850658628709941", "205350233796536871", "11856632842453069491", "736988120901130761297", "49073265311942508067185", "3485242354486865203370931", "263004127262410708414755135" ]
[ "nonn" ]
14
0
2
[ "A162695", "A380407", "A380425", "A380426", "A380427" ]
null
Seiichi Manyama, Jan 24 2025
2025-01-24T12:00:01
oeisdata/seq/A380/A380426.seq
72b84690f916cdd34a3f03c4fb6262a7
A380427
E.g.f. A(x) satisfies A(x) = exp( -x/A(x) * exp(x/A(x)) ).
[ "1", "-1", "-3", "-19", "-211", "-3301", "-66581", "-1643587", "-47986247", "-1617313033", "-61796668969", "-2639583958111", "-124635062782187", "-6446216079166189", "-362427406400015165", "-22008570202561166491", "-1435560535563493528591", "-100100185675457848764433", "-7430481272601559979203409" ]
[ "sign" ]
14
0
3
[ "A162695", "A357247", "A380425", "A380426", "A380427" ]
null
Seiichi Manyama, Jan 24 2025
2025-01-24T11:59:39
oeisdata/seq/A380/A380427.seq
c46d3a3dfef678856d7c3a6deafba2c9
A380428
Numbers k for which nonnegative integers x and y exist such that k is the concatenation of x and y as well as k = (x + y)^2.
[ "81", "100", "2025", "3025", "88209", "494209", "4941729", "7441984", "24502500", "25502500", "52881984", "60481729", "300814336", "493817284", "6049417284", "6832014336", "20408122449", "21948126201", "33058148761", "35010152100", "43470165025", "101558217124", "108878221089", "123448227904", "127194229449", "152344237969" ]
[ "nonn", "base", "easy" ]
20
1
1
[ "A000290", "A115527", "A115528", "A115529", "A115530", "A115531", "A115532", "A115533", "A115534", "A115535", "A115536", "A115537", "A115538", "A115539", "A115540", "A115541", "A115542", "A115543", "A115544", "A115545", "A115546", "A115547", "A115548", "A115549", "A115550", "A115551", "A115552", "A115553", "A115554", "A115555", "A115556", "A238712", "A380428" ]
null
Felix Huber, Jan 25 2025
2025-04-27T15:04:21
oeisdata/seq/A380/A380428.seq
555489bdf2d867c10b3e49b5b7298c85
A380429
Ulam numbers sandwiched between twin prime numbers.
[ "4", "6", "18", "72", "102", "138", "180", "282", "522", "1020", "1032", "1230", "1428", "2112", "2550", "3390", "3918", "3930", "4260", "4800", "5880", "6552", "6870", "7950", "9240", "12162", "13692", "13758", "14322", "15138", "15642", "15732", "18918", "19698", "21738", "22962", "23028", "23742", "26730", "27282", "30090" ]
[ "nonn" ]
12
1
1
[ "A001097", "A002858", "A014574", "A380429" ]
null
Massimo Kofler, Jan 24 2025
2025-02-07T00:48:13
oeisdata/seq/A380/A380429.seq
8eedcc40f6c020b8bc71601009b6cb18
A380430
Number of powerful numbers k that are not powers of primes (i.e., k is in A286708) that do not exceed the primorial number A002110(n).
[ "0", "0", "0", "0", "7", "50", "254", "1245", "5898", "29600", "163705", "925977", "5690175", "36681963", "241663896", "1662446097", "12134853382", "93406989325", "730785520398", "5990426525483", "50538885715526", "432266550168097", "3845700235189327", "35065304557027821", "334652745159828239", "3262707438761612651" ]
[ "nonn", "hard" ]
13
0
5
[ "A001694", "A126706", "A246547", "A286708", "A380254", "A380402", "A380430" ]
null
Michael De Vlieger, Jan 24 2025
2025-02-25T13:13:43
oeisdata/seq/A380/A380430.seq
b908f58f397c473ff838b3c4fdfbde0a
A380431
Number of powerful numbers that are not powers of primes (i.e. are in A286708) that do not exceed 2^n.
[ "0", "0", "0", "0", "0", "0", "1", "4", "9", "17", "28", "48", "75", "115", "178", "266", "403", "590", "865", "1263", "1830", "2644", "3810", "5466", "7838", "11210", "16011", "22841", "32530", "46315", "65886", "93658", "133060", "188952", "268204", "380564", "539823", "765481", "1085224", "1538194", "2179816", "3088481", "4375308", "6197420", "8777222" ]
[ "nonn", "hard" ]
12
0
8
[ "A001694", "A036386", "A062762", "A246547", "A286708", "A372403", "A380431" ]
null
Michael De Vlieger, Jan 24 2025
2025-01-31T04:27:03
oeisdata/seq/A380/A380431.seq
98c5d3fd1a635dbc6635e46fedf39f7f
A380432
Numbers k such that bigomega(k) > omega(k) > 3.
[ "420", "630", "660", "780", "840", "924", "990", "1020", "1050", "1092", "1140", "1170", "1260", "1320", "1380", "1386", "1428", "1470", "1530", "1540", "1560", "1596", "1638", "1650", "1680", "1710", "1716", "1740", "1820", "1848", "1860", "1890", "1932", "1950", "1980", "2040", "2070", "2100", "2142", "2184", "2220", "2244", "2280", "2340", "2380" ]
[ "nonn", "easy" ]
5
1
1
[ "A001221", "A001222", "A126706", "A200521", "A375055", "A380432" ]
null
Michael De Vlieger, Jan 29 2025
2025-01-29T12:22:40
oeisdata/seq/A380/A380432.seq
bf99f68d080e5f23305659e88e5e5ea4
A380433
Numbers that are a sum of both four and six consecutive prime numbers.
[ "72", "660", "724", "1788", "1956", "3300", "3348", "3528", "4280", "4520", "4920", "5064", "5250", "7764", "8412", "8598", "9210", "9378", "9456", "9920", "10134", "10974", "11256", "12054", "12762", "13830", "14106", "14184", "14294", "14826", "18180", "18600", "18876", "19380", "19922", "20344", "20900", "21636", "21728", "22286", "22608" ]
[ "nonn" ]
13
1
1
[ "A034963", "A127333", "A380433" ]
null
Andrej Jakobcic, Jan 24 2025
2025-02-07T13:49:36
oeisdata/seq/A380/A380433.seq
c8e81a2144c2e699eda90bc1e4670a66
A380434
Lexicographically earliest sequence of distinct positive integers such that for any n > 0, the initial digit of n divides a(n) or the initial digit of a(n) divides n.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "22", "21", "24", "23", "26", "25", "28", "27", "30", "29", "33", "36", "31", "39", "42", "32", "45", "48", "34", "40", "44", "35", "52", "41", "37", "56", "60", "38", "64", "50", "55", "43", "65", "61", "51", "46", "70", "75", "80", "47", "54", "66", "71", "49", "53", "62", "72" ]
[ "nonn", "base" ]
10
1
2
[ "A000030", "A375758", "A380434" ]
null
Rémy Sigrist, Jan 24 2025
2025-01-27T09:58:59
oeisdata/seq/A380/A380434.seq
16d38d7a496595e9c5af8b39a4c4fe0a
A380435
Erase digit 0 from decimal expansion of n. Then repeatedly apply the number of divisor function (A000005) onto each digit until a stationary value is reached. a(n) is the final stationary value (if it is reached for all digits).
[ "1", "2", "2", "2", "2", "2", "2", "2", "2", "1", "11", "12", "12", "12", "12", "12", "12", "12", "12", "2", "21", "22", "22", "22", "22", "22", "22", "22", "22", "2", "21", "22", "22", "22", "22", "22", "22", "22", "22", "2", "21", "22", "22", "22", "22", "22", "22", "22", "22", "2", "21", "22", "22", "22", "22", "22", "22", "22", "22", "2", "21", "22", "22", "22", "22", "22", "22", "22", "22", "2", "21", "22", "22", "22", "22", "22" ]
[ "nonn", "base" ]
10
1
2
[ "A002275", "A002276", "A002283", "A004719", "A007931", "A111066", "A380435" ]
null
Ctibor O. Zizka, Jan 24 2025
2025-01-25T12:39:49
oeisdata/seq/A380/A380435.seq
a62fc0966951f955159d36a7a6f83fe6
A380436
Integers with at least 1 proper factorization for which the sum of the squares of the factors is a square.
[ "12", "16", "32", "36", "48", "60", "80", "81", "96", "108", "112", "120", "128", "140", "144", "168", "192", "220", "224", "240", "252", "256", "288", "300", "320", "336", "351", "360", "364", "396", "400", "420", "432", "448", "480", "486", "500", "512", "528", "540", "544", "560", "576", "588", "608", "612", "624", "625", "640", "644", "648", "660", "672", "704" ]
[ "nonn" ]
10
1
1
[ "A118903", "A380436" ]
null
Charles L. Hohn, Jan 24 2025
2025-03-21T20:37:03
oeisdata/seq/A380/A380436.seq
30def977cda6003d071544dcd2c13201
A380437
Integers with at least 1 proper factorization for which the sum of the squares of the factors is a square, whose square root is also a factor of that number.
[ "16", "108", "192", "240", "256", "300", "576", "768", "864", "960", "1024", "1080", "1152", "1200", "1260", "1296", "1344", "1350", "1458", "1500", "1680", "1836", "2016", "2160", "2304", "2400", "2592", "2688", "2700", "2772", "2800", "2880", "2916", "3024", "3240", "3264", "3344", "3510", "3600", "3780", "3840", "4096", "4400", "4608", "4800" ]
[ "nonn" ]
8
1
1
[ "A380436", "A380437" ]
null
Charles L. Hohn, Jan 24 2025
2025-03-16T18:24:48
oeisdata/seq/A380/A380437.seq
6bf59989e5aa98ed7203dcbdd9619c87
A380438
Integers k that are the product of 3 distinct primes, the smallest of which is larger than the 5th root of k: k = p*q*r, where p, q, r are primes and k^(1/5) < p < q < r.
[ "30", "105", "165", "195", "231", "385", "455", "595", "665", "715", "805", "935", "1001", "1015", "1045", "1085", "1105", "1235", "1265", "1295", "1309", "1435", "1463", "1495", "1505", "1547", "1595", "1615", "1645", "1705", "1729", "1771", "1855", "1885", "1955", "2015", "2035", "2065", "2093", "2135", "2185", "2233", "2255", "2261", "2345", "2365", "2387", "2405", "2431", "2465", "2485" ]
[ "nonn" ]
63
1
1
[ "A007304", "A046301", "A115957", "A138109", "A251728", "A253567", "A290965", "A362910", "A379271", "A380438", "A380995" ]
null
Matthew Goers, Jan 24 2025
2025-05-27T08:11:42
oeisdata/seq/A380/A380438.seq
b75a150ebd9866b262f85c20844f9cbd
A380439
a(n) = 1 if A003557(n)^2 > n, otherwise 0, where A003557(n) is n divided by its squarefree kernel.
[ "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1" ]
[ "nonn" ]
16
1
null
[ "A003557", "A059172", "A380439" ]
null
Antti Karttunen, Jan 27 2025
2025-06-22T09:18:30
oeisdata/seq/A380/A380439.seq
81b332877ef250331cf9b25bf4c62838
A380440
a(n) = 1 if n has no squarefree divisor d such that d^2 > n, otherwise 0.
[ "1", "0", "0", "1", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "1" ]
[ "nonn" ]
9
1
null
[ "A005117", "A341645", "A380440" ]
null
Antti Karttunen, Jan 27 2025
2025-01-27T16:50:18
oeisdata/seq/A380/A380440.seq
15a8e10ab2471b94e1bb8aab891c1f42
A380441
Sum of the nonprimes dividing n and the number of distinct primes dividing n.
[ "1", "2", "2", "6", "2", "9", "2", "14", "11", "13", "2", "25", "2", "17", "18", "30", "2", "36", "2", "37", "24", "25", "2", "57", "27", "29", "38", "49", "2", "65", "2", "62", "36", "37", "38", "88", "2", "41", "42", "85", "2", "87", "2", "73", "72", "49", "2", "121", "51", "88", "54", "85", "2", "117", "58", "113", "60", "61", "2", "161", "2", "65", "96", "126", "68", "131", "2", "109", "72", "133", "2", "192", "2", "77", "118", "121", "80", "153", "2", "181", "119", "85", "2", "215", "88", "89", "90", "169", "2", "227", "94", "145", "96" ]
[ "nonn", "easy" ]
21
1
2
[ "A000203", "A001221", "A005171", "A005451", "A008472", "A380441" ]
null
Wesley Ivan Hurt, Jun 21 2025
2025-07-02T16:29:03
oeisdata/seq/A380/A380441.seq
6c6ef61ce3c0b84987fd3d115fee7f36
A380443
a(n) = numerator(b(n)), where b(n) = b(n/2)/2 for n even and 1 - b((n-1)/2)/2 for n odd with b(1) = 1.
[ "1", "1", "1", "1", "3", "1", "3", "1", "7", "3", "5", "1", "7", "3", "5", "1", "15", "7", "9", "3", "13", "5", "11", "1", "15", "7", "9", "3", "13", "5", "11", "1", "31", "15", "17", "7", "25", "9", "23", "3", "29", "13", "19", "5", "27", "11", "21", "1", "31", "15", "17", "7", "25", "9", "23", "3", "29", "13", "19", "5", "27", "11", "21", "1", "63", "31", "33", "15", "49", "17", "47", "7", "57", "25", "39" ]
[ "nonn", "easy", "frac", "look" ]
24
1
5
[ "A053644", "A380443" ]
null
Stefano Spezia, Jun 21 2025
2025-06-22T16:30:46
oeisdata/seq/A380/A380443.seq
902be683faf402a75f3ef60c4f3b6a52
A380444
Sum of the nonprimes dividing n and the squares of the primes dividing n.
[ "1", "5", "10", "9", "26", "20", "50", "17", "19", "40", "122", "36", "170", "68", "50", "33", "290", "47", "362", "64", "80", "148", "530", "68", "51", "200", "46", "100", "842", "100", "962", "65", "164", "328", "110", "99", "1370", "404", "218", "112", "1682", "146", "1850", "196", "104", "580", "2210", "132", "99", "115", "350", "256", "2810", "128", "202", "164", "428", "904", "3482", "196", "3722", "1028", "152", "129", "260", "262", "4490", "400", "608", "208", "5042", "203", "5330", "1448", "150", "484" ]
[ "nonn", "easy" ]
28
1
2
[ "A000005", "A000203", "A005063", "A008472", "A010051", "A023890", "A103164", "A380444" ]
null
Wesley Ivan Hurt, Jun 21 2025
2025-07-02T17:08:45
oeisdata/seq/A380/A380444.seq
539afd85738db2a924fd67cd696fcd11
A380445
a(n) = 10*binomial(n,5) + 6*binomial(n,4) + binomial(n,3) + binomial(n,2).
[ "0", "0", "1", "4", "16", "60", "185", "476", "1064", "2136", "3945", "6820", "11176", "17524", "26481", "38780", "55280", "76976", "105009", "140676", "185440", "240940", "309001", "391644", "491096", "609800", "750425", "915876", "1109304", "1334116", "1593985", "1892860", "2234976", "2624864", "3067361", "3567620", "4131120", "4763676" ]
[ "nonn", "easy" ]
19
0
4
[ "A380445", "A383797" ]
null
Enrique Navarrete, Jun 21 2025
2025-06-25T11:27:50
oeisdata/seq/A380/A380445.seq
1eaeab40f38da353e38a8950a5f096fe
A380447
Number of primes dividing n plus n times the number of nonprimes dividing n.
[ "1", "3", "4", "9", "6", "14", "8", "25", "19", "22", "12", "50", "14", "30", "32", "65", "18", "74", "20", "82", "44", "46", "24", "146", "51", "54", "82", "114", "30", "153", "32", "161", "68", "70", "72", "254", "38", "78", "80", "242", "42", "213", "44", "178", "182", "94", "48", "386", "99", "202", "104", "210", "54", "326", "112", "338", "116", "118", "60", "543", "62", "126", "254", "385", "132", "333", "68", "274", "140", "353", "72", "722", "74", "150", "302", "306", "156", "393", "80", "642", "325", "166" ]
[ "nonn", "easy" ]
25
1
2
[ "A000005", "A001221", "A005171", "A380447" ]
null
Wesley Ivan Hurt, Jun 21 2025
2025-07-02T15:47:25
oeisdata/seq/A380/A380447.seq
090fa469a90d98548ec93bb27457f44c
A380448
Least primes which can be represented as the sum of distinct positive cubes in exactly n ways, or 0 if no such prime exists.
[ "73", "757", "953", "2521", "1801", "3257", "2953", "4013", "4139", "4789", "5347", "4481", "5669", "4663", "6427", "6659", "5867", "6301", "6841", "7867", "7687", "7741", "10169", "7057", "7723", "7561", "9631", "8443", "8191", "8387", "9883", "10079", "10313", "10891", "10729", "10009", "9109", "10711", "9829", "11161", "10457", "12547", "11699", "10513", "10333", "11159", "13007" ]
[ "nonn" ]
38
1
1
[ "A003997", "A275154", "A380448", "A385094" ]
null
Zhining Yang, Jun 21 2025
2025-07-02T11:34:55
oeisdata/seq/A380/A380448.seq
fc4c82c7f3d3c1ffad3f9e4bc392ea44
A380449
Sum of the divisors of n plus the number of nonprime divisors of n.
[ "2", "4", "5", "9", "7", "14", "9", "18", "15", "20", "13", "32", "15", "26", "26", "35", "19", "43", "21", "46", "34", "38", "25", "66", "33", "44", "43", "60", "31", "77", "33", "68", "50", "56", "50", "98", "39", "62", "58", "96", "43", "101", "45", "88", "82", "74", "49", "132", "59", "97", "74", "102", "55", "126", "74", "126", "82", "92", "61", "177", "63", "98", "108", "133", "86", "149", "69", "130", "98", "149", "73", "205", "75", "116", "128", "144", "98", "173", "81", "194", "125", "128", "85", "233", "110", "134", "122" ]
[ "nonn", "easy" ]
26
1
1
[ "A000005", "A000203", "A001221", "A033273", "A113636", "A380449" ]
null
Wesley Ivan Hurt, Jun 21 2025
2025-07-02T16:17:56
oeisdata/seq/A380/A380449.seq
0fb52974f89fc5340c5313f9b8e1b4a0
A380450
Number of integers k such that prime(n) - primorial(k) is prime.
[ "0", "1", "1", "1", "1", "2", "1", "2", "1", "1", "1", "2", "1", "3", "2", "2", "2", "2", "2", "1", "3", "1", "1", "2", "1", "1", "3", "1", "3", "2", "1", "1", "2", "2", "0", "1", "2", "1", "1", "1", "2", "2", "0", "2", "2", "2", "1", "2", "2", "4", "2", "2", "3", "1", "3", "3", "3", "3", "2", "2", "3", "2", "2", "2", "4", "2", "0", "3", "2", "2", "1", "2", "2", "2", "2", "2", "3", "1", "1", "2", "1", "2", "1", "2", "3", "1", "3", "0", "2", "3" ]
[ "nonn" ]
52
1
6
[ "A000040", "A002110", "A115785", "A175974", "A380450", "A385210" ]
null
Daniel D Gibson, Jun 22 2025
2025-06-28T09:19:39
oeisdata/seq/A380/A380450.seq
035fd9697356890f066ad3bd76170f1a
A380451
Number of disjoint-path coverings for 2 X n rectangular grids, admitting zero-length paths.
[ "2", "15", "95", "604", "3835", "24349", "154594", "981531", "6231827", "39566420", "251210695", "1594958889", "10126534850", "64294264119", "408209961239", "2591761096236", "16455320099427", "104476280613925", "663329132764770", "4211535247894499", "26739409243687915", "169770870862086564", "1077890252944724559", "6843620413168932241", "43450750418785228802" ]
[ "nonn", "easy", "changed" ]
36
1
1
[ "A003763", "A380451" ]
null
Anton M. Alekseev, Jun 22 2025
2025-07-06T15:02:53
oeisdata/seq/A380/A380451.seq
adce00a256ff96297edb960adaa3ffe6
A380453
Number of dessins d'enfants D(n,g) with n edges of genus g, read by rows.
[ "1", "3", "6", "1", "20", "6", "60", "33", "4", "291", "285", "48", "1310", "2115", "708", "30", "6975", "16533", "9807", "1155", "37746", "126501", "119436", "29910", "900", "215602", "972441", "1355400", "601364", "58032", "1262874", "7451679", "14561360", "10260804", "2112300", "54990", "7611156", "57167260", "150429819", "156469887", "57017238", "4764654" ]
[ "nonn", "tabf" ]
46
1
2
[ "A057005", "A090371", "A118094", "A214819", "A214820", "A321710", "A356694", "A380453" ]
null
Paawan Jethva, Jun 22 2025
2025-06-28T11:50:22
oeisdata/seq/A380/A380453.seq
d55cf4ae0c341915fce044bf0cf97175
A380454
a(n) = 1 if the product of exponents in its prime factorization is greater than 3, otherwise 0.
[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1" ]
[ "nonn" ]
27
1
null
[ "A000005", "A001221", "A005361", "A034444", "A046951", "A048105", "A048106", "A048111", "A059956", "A085548", "A359471", "A359472", "A380454" ]
null
Antti Karttunen, Jan 27 2025
2025-01-30T05:07:33
oeisdata/seq/A380/A380454.seq
613878f2918b4350dbd51140bf9013ea
A380457
Sum of the divisors of n plus the number of distinct primes dividing n.
[ "1", "4", "5", "8", "7", "14", "9", "16", "14", "20", "13", "30", "15", "26", "26", "32", "19", "41", "21", "44", "34", "38", "25", "62", "32", "44", "41", "58", "31", "75", "33", "64", "50", "56", "50", "93", "39", "62", "58", "92", "43", "99", "45", "86", "80", "74", "49", "126", "58", "95", "74", "100", "55", "122", "74", "122", "82", "92", "61", "171", "63", "98", "106", "128", "86", "147", "69", "128", "98", "147", "73", "197", "75", "116", "126", "142", "98", "171", "81", "188", "122", "128", "85", "227", "110", "134", "122" ]
[ "nonn", "easy" ]
20
1
2
[ "A000203", "A001221", "A014683", "A380457" ]
null
Wesley Ivan Hurt, Jun 22 2025
2025-07-02T16:34:09
oeisdata/seq/A380/A380457.seq
f8d3aa4873c85258919436cebc2b00be
A380458
Characteristic function of A337533 (union of {1} with nonsquares whose square part's square root is in the sequence).
[ "1", "1", "1", "0", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "0", "0", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "0", "0", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "1", "0" ]
[ "nonn" ]
7
1
null
[ "A209229", "A267116", "A337533", "A337534", "A380458" ]
null
Antti Karttunen, Jan 27 2025
2025-01-27T16:45:34
oeisdata/seq/A380/A380458.seq
6696f5d0e9e77d10fbd5d9150912d88c
A380459
a(n) = Product_{d|n} A276086(d)^A349394(n/d).
[ "1", "2", "2", "12", "2", "18", "2", "1296", "48", "54", "2", "1620", "2", "30", "108", "25194240", "2", "4050", "2", "131220", "60", "270", "2", "12150000", "576", "150", "3317760", "67500", "2", "33750", "2", "142818689064960000", "540", "1350", "180", "2050312500", "2", "750", "300", "1195742250000", "2", "281250", "2", "82012500", "26244000", "6750", "2", "92264062500000000", "1280", "13668750", "2700", "42187500", "2" ]
[ "nonn" ]
7
1
2
[ "A003415", "A276085", "A276086", "A329350", "A329380", "A349394", "A380459", "A380460" ]
null
Antti Karttunen, Jan 31 2025
2025-01-31T21:12:15
oeisdata/seq/A380/A380459.seq
742250b8e57ed53b958f1bac6cc7fe64
A380460
Lexicographically earliest infinite sequence such that a(i) = a(j) => A380459(i) = A380459(j), for all i, j >= 1, where A380459(n) = Product_{d|n} A276086(d)^A349394(n/d).
[ "1", "2", "2", "3", "2", "4", "2", "5", "6", "7", "2", "8", "2", "9", "10", "11", "2", "12", "2", "13", "14", "15", "2", "16", "17", "18", "19", "20", "2", "21", "2", "22", "23", "24", "25", "26", "2", "27", "28", "29", "2", "30", "2", "31", "32", "33", "2", "34", "35", "36", "37", "38", "2", "39", "8", "40", "41", "21", "2", "42", "2", "43", "44", "45", "46", "47", "2", "48", "49", "50", "2", "51", "2", "52", "53", "54", "46", "55", "2", "56", "57", "58", "2", "59", "60", "61", "20", "62", "2", "63", "64", "65", "66", "67", "68", "69", "2", "70", "71" ]
[ "nonn" ]
10
1
2
[ "A003415", "A276086", "A305800", "A329351", "A329381", "A349394", "A380459", "A380460", "A380467", "A380477" ]
null
Antti Karttunen, Jan 31 2025
2025-02-03T11:55:01
oeisdata/seq/A380/A380460.seq
5cf71b1f6c62bceb563333a9dc6ccba0
A380461
Number of edge covers of fan graph F_{2,n}.
[ "1", "16", "154", "1289", "10180", "78372", "596337", "4512900", "34064998", "256825009", "1935169456", "14577526976", "109797758833", "826945679592", "6227993359362", "46904386459065", "353244994467916", "2660340755025580", "20035394638446769", "150889230111278492", "1136366561949728110" ]
[ "nonn", "easy" ]
23
1
2
null
null
Feryal Alayont, Jun 22 2025
2025-06-24T13:30:38
oeisdata/seq/A380/A380461.seq
0adb6bd015db7b4a76fb971e32a84b94
A380462
a(n) is the number of positive solutions to the Diophantine equation w^2 + x^2 + y^2 + z^2 = w*x*y*z such that x,y,z,w < e^n.
[ "1", "2", "2", "3", "4", "6", "6", "7", "10", "12", "16", "17", "18", "23", "25", "32", "35", "39", "43", "47", "55", "60", "64", "73", "76", "86", "94", "101", "111", "118", "132", "141", "150", "159", "168", "180", "192", "203", "220", "235", "247", "261", "275", "289", "302", "324", "340", "361", "376", "394", "413", "433", "454", "472", "498", "518", "536", "560", "584", "606", "632", "658", "684" ]
[ "nonn" ]
37
1
2
[ "A061292", "A380462" ]
null
Bence Bernáth, Jun 22 2025
2025-07-01T10:53:55
oeisdata/seq/A380/A380462.seq
a397cfadcb30bc8b9bcd2381af955582
A380463
Partial sums of floor(n^2/13).
[ "0", "0", "0", "0", "1", "2", "4", "7", "11", "17", "24", "33", "44", "57", "72", "89", "108", "130", "154", "181", "211", "244", "281", "321", "365", "413", "465", "521", "581", "645", "714", "787", "865", "948", "1036", "1130", "1229", "1334", "1445", "1562", "1685", "1814", "1949", "2091", "2239", "2394", "2556", "2725", "2902", "3086", "3278", "3478" ]
[ "nonn", "easy" ]
24
0
6
[ "A173645", "A173653", "A175724", "A380463" ]
null
Hoang Xuan Thanh, Jun 22 2025
2025-06-25T07:58:37
oeisdata/seq/A380/A380463.seq
7482d49820d787d83d30d3ac51cdb10f
A380464
Integers k such that A005245(m*k) < A005245(k) for some m.
[ "1499", "1823", "3767", "5468", "5469", "13163", "13487", "16403", "16407", "20507", "25799", "28607", "30713", "30983", "32828", "36383" ]
[ "nonn", "more" ]
28
1
1
[ "A005245", "A195101", "A350723", "A351467", "A380464" ]
null
John M. Campbell, Jun 22 2025
2025-07-03T01:01:30
oeisdata/seq/A380/A380464.seq
8b85cd530f5451e1477f1c107ce5d2b7
A380465
G.f. A(x) satisfies A(x) = 1/( 1 - 25*x*A(x)^2 )^(1/5).
[ "1", "5", "125", "4250", "166250", "7052500", "315459375", "14648437500", "699404062500", "34120414453125", "1693355782421875", "85222795492187500", "4339218139648437500", "223115431527734375000", "11568972340119140625000", "604249120575386718750000", "31761084429202554931640625", "1678825356066226959228515625" ]
[ "nonn" ]
23
0
2
[ "A034688", "A078534", "A380465", "A380466", "A380471", "A385203", "A385204", "A385205" ]
null
Seiichi Manyama, Jun 23 2025
2025-06-23T10:12:48
oeisdata/seq/A380/A380465.seq
9d3253da6f0dd5ac0e9afb215c5e3a97
A380466
G.f. A(x) satisfies A(x) = 1/( 1 - 25*x*A(x)^3 )^(1/5).
[ "1", "5", "150", "6250", "301875", "15868125", "881237500", "50865750000", "3021240234375", "183454158593750", "11336659803906250", "710625236343750000", "45075347315400390625", "2887845039367675781250", "186601230428607421875000", "12146710229056792968750000", "795792421294273872070312500" ]
[ "nonn" ]
24
0
2
[ "A034688", "A078534", "A380465", "A380466", "A380471", "A385203", "A385204", "A385205" ]
null
Seiichi Manyama, Jun 23 2025
2025-06-23T10:12:51
oeisdata/seq/A380/A380466.seq
ce7d3bb88c69d58c5d8d59bf26904775
A380467
a(n) = 1 if A380459(n) has no divisors of form p^p, otherwise 0.
[ "1", "1", "1", "0", "1", "1", "1", "0", "0", "0", "1", "0", "1", "1", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "1", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0" ]
[ "nonn" ]
10
1
null
[ "A008966", "A276086", "A349394", "A359550", "A380459", "A380467", "A380468", "A380469" ]
null
Antti Karttunen, Feb 01 2025
2025-02-03T09:50:21
oeisdata/seq/A380/A380467.seq
952c5455c54fb40f50e475837e07e2e6
A380468
Numbers k such that A380459(k) has no divisors of the form p^p, for any prime p.
[ "1", "2", "3", "5", "6", "7", "11", "13", "14", "17", "19", "23", "26", "29", "31", "37", "38", "41", "43", "47", "53", "59", "61", "62", "67", "71", "73", "74", "79", "83", "86", "89", "97", "101", "103", "107", "109", "113", "122", "127", "131", "134", "137", "139", "146", "149", "151", "157", "158", "163", "167", "173", "179", "181", "186", "191", "193", "194", "197", "199", "206", "211", "218", "223", "227", "229", "233", "239", "241", "251", "254" ]
[ "nonn" ]
25
1
2
[ "A005117", "A048103", "A276086", "A359550", "A380459", "A380467", "A380468", "A380470", "A380474", "A380475", "A380478" ]
null
Antti Karttunen, Feb 01 2025
2025-02-03T17:02:21
oeisdata/seq/A380/A380468.seq
4165bc6d91f48accab8f15047b6807c6
A380469
a(n) = 1 if n is squarefree, but A380459(n) has a factor of the form p^p, otherwise 0.
[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "1", "1", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "1", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "1", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "1", "1", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1" ]
[ "nonn" ]
7
1
null
[ "A008966", "A048103", "A359550", "A380459", "A380467", "A380469", "A380470" ]
null
Antti Karttunen, Feb 02 2025
2025-02-02T10:57:52
oeisdata/seq/A380/A380469.seq
c76177c0df5d66d8a380d6162287eff8
A380470
Numbers k that are squarefree, but A380459(k) is not in A048103.
[ "10", "15", "21", "22", "30", "33", "34", "35", "39", "42", "46", "51", "55", "57", "58", "65", "66", "69", "70", "77", "78", "82", "85", "87", "91", "93", "94", "95", "102", "105", "106", "110", "111", "114", "115", "118", "119", "123", "129", "130", "133", "138", "141", "142", "143", "145", "154", "155", "159", "161", "165", "166", "170", "174", "177", "178", "182", "183", "185", "187", "190", "195", "201", "202", "203", "205", "209", "210", "213" ]
[ "nonn" ]
15
1
1
[ "A005117", "A380468", "A380469", "A380470", "A380528", "A380530" ]
null
Antti Karttunen, Feb 02 2025
2025-05-09T16:19:20
oeisdata/seq/A380/A380470.seq
efe58c51a263aa78cc72df78816f527e
A380471
G.f. A(x) satisfies A(x) = 1/( 1 - 25*x*A(x)^4 )^(1/5).
[ "1", "5", "175", "8625", "495000", "30980625", "2050781250", "141187921875", "10006590468750", "725240531640625", "53503504196484375", "4004478454589843750", "303320955472031250000", "23207794539155419921875", "1791025435519151367187500", "139250846557940616210937500", "10897102765738964080810546875" ]
[ "nonn" ]
22
0
2
[ "A034688", "A078534", "A380465", "A380466", "A380471", "A385203", "A385204", "A385205" ]
null
Seiichi Manyama, Jun 23 2025
2025-06-23T10:12:54
oeisdata/seq/A380/A380471.seq
665dbbf1fc751a205e240e57f8af927f
A380472
a(n) = gcd_{primes P >= prime(n+1)} Product_{i=1..n} (P^2-i^2).
[ "1", "24", "360", "40320", "1814400", "479001600", "43589145600", "20922789888000", "3201186852864000", "2432902008176640000", "562000363888803840000", "620448401733239439360000", "201645730563302817792000000", "304888344611713860501504000000", "132626429906095529318154240000000", "263130836933693530167218012160000000" ]
[ "nonn", "easy" ]
70
0
2
[ "A014634", "A014635", "A084920", "A380472" ]
null
Lily Bétaz, Martin Chevalier, and Basile Fusil, Jun 23 2025
2025-07-03T09:17:37
oeisdata/seq/A380/A380472.seq
aad9e6d11e911b78d684ca7b748fe868
A380474
Numbers k such that A380459(k) has no divisors of the form p^p, while A003415(k) has such a divisor or is 0.
[ "1", "158", "482", "698", "914", "1238", "1346", "1454", "1994", "2102", "2426", "2642", "2858", "2966", "3398", "3506", "3722", "4262", "4478", "4586", "4694", "5234", "5342", "5666", "5774", "6098", "6638", "6746", "7286", "7394", "7934", "8042", "8258", "9014", "9122", "9446", "9662", "9986", "10202", "10418", "10958", "11282", "11498", "11714", "12146", "12686", "12794", "12902" ]
[ "nonn" ]
26
1
2
[ "A003415", "A039956", "A047257", "A048103", "A141964", "A276086", "A327929", "A327934", "A358215", "A380459", "A380468", "A380474", "A380478" ]
null
Antti Karttunen, Feb 02 2025
2025-02-03T19:56:31
oeisdata/seq/A380/A380474.seq
345097225f473403f609f6bd6722b39d
A380475
a(n) is the least term in A380468 that has exactly n prime factors.
[ "1", "2", "6", "186", "4686" ]
[ "nonn", "hard", "more" ]
38
0
2
[ "A001221", "A001222", "A003415", "A047247", "A047257", "A048103", "A049345", "A276086", "A317836", "A358235", "A380459", "A380468", "A380475", "A380476", "A380525", "A380528", "A380530" ]
null
Antti Karttunen, Feb 03 2025
2025-02-19T10:25:41
oeisdata/seq/A380/A380475.seq
db69aeed21b76f1e9ff07fe8650dedd2
A380476
Numbers k with at least 4 prime factors such that A380459(k) is in A048103, i.e., has no divisors of the form p^p.
[ "4686", "32406", "184866", "209166", "388086", "1099626", "1714866", "2111406", "2166846", "2356206", "3081606", "3303366", "6445806", "11366106", "21621606", "23022366", "39824466", "39826986", "42882846", "43197846", "46043826", "58216686", "61265886", "63603546", "66496506", "66611166", "87941706", "88968246", "92086746", "97117026", "101108706", "103367886", "118743306", "119658066" ]
[ "nonn" ]
41
1
1
[ "A001222", "A002476", "A003415", "A005117", "A007528", "A033987", "A046386", "A047247", "A047257", "A048103", "A276086", "A317836", "A349394", "A358235", "A358673", "A380459", "A380467", "A380468", "A380475", "A380476", "A380478", "A380526", "A380528", "A380530" ]
null
Antti Karttunen, Feb 04 2025
2025-02-19T10:25:45
oeisdata/seq/A380/A380476.seq
1706c323cd5b0d36fedaa9d068450a98
A380477
a(n) = 1 if n is not a prime, and A380459(n) has no divisors of form p^p, otherwise 0.
[ "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0" ]
[ "nonn" ]
8
1
null
[ "A010051", "A048103", "A359550", "A380459", "A380467", "A380477", "A380478" ]
null
Antti Karttunen, Feb 03 2025
2025-02-03T11:09:14
oeisdata/seq/A380/A380477.seq
1b5c3eafc5288c970d91a9d1d199dcda
A380478
Nonprime numbers k such that A380459(k) has no divisors of form p^p.
[ "1", "6", "14", "26", "38", "62", "74", "86", "122", "134", "146", "158", "186", "194", "206", "218", "254", "278", "302", "314", "326", "362", "386", "398", "422", "434", "446", "458", "482", "542", "554", "566", "614", "626", "662", "674", "698", "734", "746", "758", "794", "818", "842", "854", "866", "878", "906", "914", "926", "974", "998", "1046", "1082", "1094", "1142", "1154", "1202", "1214", "1226", "1238", "1262", "1266", "1286" ]
[ "nonn" ]
19
1
2
[ "A000469", "A018252", "A039956", "A048103", "A276086", "A380459", "A380468", "A380474", "A380477", "A380478" ]
null
Antti Karttunen, Feb 03 2025
2025-02-03T17:03:06
oeisdata/seq/A380/A380478.seq
c942ee49f64ab87d1c27ec861eff7643
A380479
Number of prime factors (with repetition) in Product_{d|n} A276086(n/d)^A349394(d).
[ "0", "1", "1", "3", "1", "3", "1", "8", "5", "4", "1", "7", "1", "3", "5", "18", "1", "7", "1", "11", "4", "5", "1", "14", "8", "4", "18", "9", "1", "8", "1", "40", "6", "6", "5", "17", "1", "5", "5", "24", "1", "9", "1", "15", "16", "7", "1", "32", "9", "13", "7", "13", "1", "21", "7", "22", "6", "8", "1", "15", "1", "3", "14", "82", "6", "9", "1", "15", "8", "10", "1", "30", "1", "4", "19", "13", "6", "10", "1", "52", "60", "6", "1", "21", "8", "5", "9", "32", "1", "18", "5", "19", "4", "7", "7", "62", "1", "15" ]
[ "nonn" ]
18
1
4
[ "A001222", "A049345", "A276086", "A276150", "A349394", "A380459", "A380479", "A380480" ]
null
Antti Karttunen, Feb 04 2025
2025-02-04T10:30:50
oeisdata/seq/A380/A380479.seq
46cb47812f0d74aa3a30e8681ae628f6
A380480
The maximal exponent in the prime factorization of Product_{d|n} A276086(n/d)^A349394(d).
[ "0", "1", "1", "2", "1", "2", "1", "4", "4", "3", "1", "4", "1", "1", "3", "9", "1", "4", "1", "8", "2", "3", "1", "5", "6", "2", "13", "4", "1", "4", "1", "20", "3", "3", "2", "8", "1", "3", "2", "14", "1", "6", "1", "8", "8", "3", "1", "14", "8", "7", "3", "8", "1", "10", "4", "13", "3", "4", "1", "9", "1", "1", "7", "41", "2", "4", "1", "8", "3", "5", "1", "18", "1", "1", "7", "7", "2", "6", "1", "30", "40", "3", "1", "14", "4", "2", "4", "14", "1", "8", "3", "8", "2", "3", "3", "27", "1", "8", "8", "14", "1", "4", "1", "20", "5" ]
[ "nonn" ]
10
1
4
[ "A051903", "A276086", "A349394", "A380459", "A380479", "A380480" ]
null
Antti Karttunen, Feb 04 2025
2025-02-04T10:30:56
oeisdata/seq/A380/A380480.seq
f91e0758f88f2d1e7ca993d2709eb96e
A380482
a(n) is the multiplicative order of -3 modulo prime(n); a(2) = 0 for completion.
[ "1", "0", "4", "3", "10", "6", "16", "9", "22", "28", "15", "9", "8", "21", "46", "52", "58", "5", "11", "70", "12", "39", "82", "88", "48", "100", "17", "106", "54", "112", "63", "130", "136", "69", "148", "25", "39", "81", "166", "172", "178", "90", "190", "16", "196", "99", "105", "111", "226", "114", "232", "238", "120", "250", "256", "262", "268", "15", "138", "280" ]
[ "nonn", "easy", "changed" ]
32
1
3
[ "A002371", "A014664", "A062117", "A082654", "A105875", "A211241", "A211242", "A211243", "A211244", "A211245", "A337878", "A380482", "A380531", "A380532", "A380533", "A380540", "A380541", "A380542", "A385222" ]
null
Jianing Song, Jun 27 2025
2025-07-07T10:43:41
oeisdata/seq/A380/A380482.seq
1eb46ea8c12cb5dc5f10d4cfce0a24a6
A380484
a(n) = 1 if n is congruent to {0, 1, 2, 3, 4, 5} mod 30, otherwise 0.
[ "1", "1", "1", "1", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "1", "1", "1", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "1", "1", "1", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "1", "1", "1", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1" ]
[ "nonn", "base", "easy" ]
23
0
null
[ "A049345", "A079998", "A276086", "A380484", "A380485", "A380486" ]
null
Antti Karttunen, Feb 03 2025
2025-06-04T15:32:29
oeisdata/seq/A380/A380484.seq
f97b7062910196ceea02578c5f91812d
A380485
Numbers congruent to {0, 1, 2, 3, 4, 5} mod 30.
[ "0", "1", "2", "3", "4", "5", "30", "31", "32", "33", "34", "35", "60", "61", "62", "63", "64", "65", "90", "91", "92", "93", "94", "95", "120", "121", "122", "123", "124", "125", "150", "151", "152", "153", "154", "155", "180", "181", "182", "183", "184", "185", "210", "211", "212", "213", "214", "215", "240", "241", "242", "243", "244", "245", "270", "271", "272", "273", "274", "275", "300", "301", "302", "303", "304", "305", "330", "331", "332", "333" ]
[ "nonn", "easy" ]
15
1
3
[ "A267711", "A276086", "A380484", "A380485", "A380486" ]
null
Antti Karttunen, Feb 03 2025
2025-02-03T19:56:09
oeisdata/seq/A380/A380485.seq
060dd7e3ebdc5f4a6bab33895b2bf7cc
A380486
Numbers not congruent to {0, 1, 2, 3, 4, 5} mod 30.
[ "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "24", "25", "26", "27", "28", "29", "36", "37", "38", "39", "40", "41", "42", "43", "44", "45", "46", "47", "48", "49", "50", "51", "52", "53", "54", "55", "56", "57", "58", "59", "66", "67", "68", "69", "70", "71", "72", "73", "74", "75", "76", "77", "78", "79", "80", "81", "82", "83", "84", "85", "86", "87", "88", "89", "96", "97", "98", "99", "100", "101", "102" ]
[ "nonn", "easy", "less" ]
11
1
1
[ "A276086", "A380484", "A380485", "A380486" ]
null
Antti Karttunen, Feb 03 2025
2025-02-03T19:56:02
oeisdata/seq/A380/A380486.seq
7adda687b079d35c30adf4cf717e3e1e
A380487
Numbers such that the sum of prime factors without repetition divides the product of prime factors without repetition and each division yields a greater quotient.
[ "2", "30", "70", "105", "231", "627", "805", "1122", "2730", "3570", "8778", "9282", "10626", "15015", "24738", "24882", "31746", "33495", "33915", "44330", "45885", "49335", "51051", "62985", "72930", "95095", "106590", "132990", "145145", "156009", "170170", "222870", "230945", "274505", "290598", "329406", "335478", "418285", "449995" ]
[ "nonn" ]
33
1
1
[ "A007947", "A008472", "A086486", "A380487" ]
null
Torlach Rush, Jan 24 2025
2025-05-02T04:21:49
oeisdata/seq/A380/A380487.seq
d4343be62f6c5ac7950a1927b3a87e75
A380488
Array read by descending antidiagonals where row n holds the lexicographically earliest sequence of distinct positive integers such that T(n,k) is a multiple of the sum of base n digits of T(n,k-1), starting from T(n,1) = 1.
[ "1", "2", "1", "3", "2", "1", "4", "4", "2", "1", "5", "6", "4", "2", "1", "6", "8", "3", "4", "2", "1", "8", "12", "6", "8", "4", "2", "1", "7", "10", "9", "12", "8", "4", "2", "1", "9", "14", "12", "16", "3", "8", "4", "2", "1", "10", "16", "15", "20", "6", "6", "8", "4", "2", "1", "12", "20", "18", "24", "5", "12", "3", "8", "4", "2", "1", "14", "24", "21", "32", "10", "18", "6", "16", "8", "4", "2", "1" ]
[ "nonn", "base", "tabl" ]
10
2
2
[ "A242704", "A380488", "A380489" ]
null
M. F. Hasler and Ali Sada, Jan 24 2025
2025-01-25T12:36:31
oeisdata/seq/A380/A380488.seq
591c162500b1fe577da624dc99c7e1f6
A380489
Index k of the first element in row n of A380488 that is a multiple of n-1.
[ "1", "2", "4", "3", "7", "5", "11", "4", "13", "8", "16", "6", "19", "12", "12", "5", "27", "14", "28", "9", "19", "17", "35", "7", "37", "20", "40", "13", "43", "13", "50", "6", "31", "28", "47", "15", "55", "29", "35", "10", "63", "20", "65", "18", "29", "36", "72", "8", "74", "38", "37", "21", "79", "41", "78", "14", "55", "44", "88", "14", "91", "51", "26", "7" ]
[ "nonn", "base" ]
12
2
2
[ "A380488", "A380489" ]
null
M. F. Hasler and Ali Sada, Jan 25 2025
2025-01-25T12:36:59
oeisdata/seq/A380/A380489.seq
3374bed4137a2014ec5e9651eb8f2ed6
A380490
Replace prime digits of n by 0's.
[ "1", "0", "0", "4", "0", "6", "0", "8", "9", "10", "11", "10", "10", "14", "10", "16", "10", "18", "19", "0", "1", "0", "0", "4", "0", "6", "0", "8", "9", "0", "1", "0", "0", "4", "0", "6", "0", "8", "9", "40", "41", "40", "40", "44", "40", "46", "40", "48", "49", "0", "1", "0", "0", "4", "0", "6", "0", "8", "9", "60", "61", "60", "60", "64", "60", "66", "60", "68", "69", "0", "1", "0", "0", "4", "0", "6", "0", "8", "9", "80", "81", "80" ]
[ "nonn", "base", "look" ]
16
1
4
[ "A046034", "A084984", "A380490" ]
null
Ctibor O. Zizka, Jan 25 2025
2025-05-21T01:35:42
oeisdata/seq/A380/A380490.seq
2fddc09ba54d61e995c6a0773e3a72c3
A380491
a(n) = n! * Sum_{k=0..n} binomial(2*n-3,k)/(n-k)!.
[ "1", "0", "3", "34", "501", "9276", "207775", "5470158", "165625929", "5671386136", "216730118331", "9144481575450", "422249317829053", "21180324426577044", "1146880568461500951", "66677192513929212166", "4142571510546929867025", "273910161452560881843888", "19204878684852222745880179" ]
[ "nonn" ]
13
0
3
[ "A082545", "A152059", "A251568", "A293985", "A343832", "A380491", "A380492", "A380493" ]
null
Seiichi Manyama, Jan 25 2025
2025-01-25T11:27:13
oeisdata/seq/A380/A380491.seq
a30e49177eeb2ab42fb0739f504625d9
A380492
a(n) = n! * Sum_{k=0..n} binomial(2*n-2,k)/(n-k)!.
[ "1", "1", "7", "73", "1045", "19081", "424051", "11109337", "335262313", "11453449105", "436944953791", "18412283563081", "849345673881277", "42570185481576793", "2303643608370636715", "133859418832759525081", "8312945340897388101841", "549460711493172343519777", "38513032385247860120975863" ]
[ "nonn" ]
10
0
3
[ "A082545", "A152059", "A251568", "A293985", "A343832", "A380491", "A380492", "A380493" ]
null
Seiichi Manyama, Jan 25 2025
2025-01-25T11:27:17
oeisdata/seq/A380/A380492.seq
41183e8baf39530ceebd366dd26047c9
A380493
a(n) = n! * Sum_{k=0..n} binomial(2*n+3,k)/(n-k)!.
[ "1", "6", "57", "748", "12585", "259026", "6315001", "178134552", "5711078673", "205209960670", "8171229107481", "357235056697476", "17014791129640057", "877089297426429738", "48657292133825026905", "2890717184573264397616", "183125115830192864360481", "12323226433255671469949622" ]
[ "nonn" ]
10
0
2
[ "A082545", "A152059", "A251568", "A293985", "A343832", "A380491", "A380492", "A380493" ]
null
Seiichi Manyama, Jan 25 2025
2025-01-25T11:27:21
oeisdata/seq/A380/A380493.seq
e4f13aa58aa1c745006d97c64ead3f93
A380494
a(1) = 1. For n > 1 a(n) is the smallest positive integer not yet in the sequence which is divisible by A007953(a(n-1)) + 1.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "12", "16", "24", "14", "18", "20", "15", "21", "28", "11", "27", "30", "32", "36", "40", "25", "48", "13", "35", "45", "50", "42", "49", "56", "60", "63", "70", "64", "22", "55", "33", "77", "75", "26", "54", "80", "72", "90", "100", "34", "88", "17", "81", "110", "39", "52", "96", "112", "65", "84", "78", "128", "108", "120", "44", "99" ]
[ "nonn", "base", "easy" ]
10
1
2
[ "A007953", "A051855", "A380494" ]
null
David James Sycamore and Ali Sada, Jan 25 2025
2025-01-29T12:47:50
oeisdata/seq/A380/A380494.seq
a0c0fc07ff98ffe32938318011bc8fee
A380495
Lexicographically earliest infinite sequence of positive integers such that consecutive occurrences of k are separated by k distinct values and each subsequence enclosed by consecutive equal values is distinct.
[ "1", "2", "1", "3", "1", "2", "4", "3", "2", "5", "6", "2", "3", "4", "2", "7", "3", "2", "5", "4", "2", "3", "8", "2", "6", "3", "2", "4", "5", "2", "3", "9", "2", "4", "3", "7", "5", "6", "3", "4", "10", "8", "3", "5", "4", "11", "3", "6", "7", "4", "3", "5", "9", "12", "3", "4", "6", "5", "3", "8", "4", "7", "3", "13", "5", "4", "3", "6", "10", "9", "3", "4", "5", "7", "3", "6", "4", "8", "3", "5", "14", "4", "3", "11", "6" ]
[ "nonn" ]
8
1
2
[ "A380278", "A380495" ]
null
Neal Gersh Tolunsky, Jan 24 2025
2025-01-27T07:31:28
oeisdata/seq/A380/A380495.seq
bb95e65b0d225241a4f62ddc138b2154
A380496
Lenstra excess of the n-th odd prime.
[ "0", "0", "1", "1", "0", "0", "4", "1", "0", "1", "0", "1", "1", "1", "1", "1", "0", "0", "0", "1", "1", "1", "1", "0", "1", "0", "1", "0", "0", "1", "0", "1", "0", "1", "0", "1", "4", "1", "0", "1", "0", "0", "0", "0", "0", "0", "1", "1", "1", "1", "0", "0", "1", "0", "1", "1", "0", "1", "0" ]
[ "nonn", "hard", "more" ]
15
1
7
null
null
Aaron N. Siegel, Jan 21 2025
2025-01-26T20:53:58
oeisdata/seq/A380/A380496.seq
3f403dc9a515f5300ced1cceade8f15d
A380497
Euler transform of primorial numbers.
[ "1", "2", "9", "46", "314", "3072", "37641", "603510", "11148030", "249327430", "7040987792", "216220333314", "7895699690498", "321315600822232", "13770543972819903", "644232544408157820", "33954066516677635554", "1994206929690480710244", "121461036181617491970561", "8111955386813996410196454", "574814471423312085719652432" ]
[ "nonn" ]
8
0
2
[ "A002110", "A030009", "A030012", "A107895", "A380497", "A380498" ]
null
Ilya Gutkovskiy, Jan 25 2025
2025-02-16T08:34:07
oeisdata/seq/A380/A380497.seq
5e934383a6574a7ff85018db6c461ecf
A380498
Inverse Euler transform of primorial numbers.
[ "2", "3", "20", "150", "1860", "24950", "444060", "8583780", "202071920", "5992771854", "186947632200", "7001535703840", "288868991951760", "12455290280427090", "587972068547997856", "31327583556941402160", "1856116108295418943020", "113366872636395265380920", "7619343577986975410930880", "541957669076266398658079700" ]
[ "nonn" ]
7
1
1
[ "A002110", "A030010", "A030011", "A112354", "A380497", "A380498" ]
null
Ilya Gutkovskiy, Jan 25 2025
2025-02-16T08:34:07
oeisdata/seq/A380/A380498.seq
f1a532004cfdbc04a313f64e47c2441a
A380499
Absolute value of the minimum coefficient of (1 - x)^2 * (1 - x^2)^2 * (1 - x^3)^2 * ... * (1 - x^n)^2.
[ "1", "2", "2", "6", "4", "12", "8", "24", "19", "44", "36", "78", "74", "148", "156", "286", "322", "556", "682", "1120", "1448", "2308", "3072", "4784", "6538", "10064", "14001", "21296", "29928", "45276", "64032", "96712", "137520", "207156", "296236", "444748", "637812", "956884", "1373622", "2062080", "2968872", "4450120", "6422472", "9616202", "13894990", "20802836" ]
[ "nonn" ]
8
0
2
[ "A002107", "A047653", "A086394", "A133871", "A369710", "A380499" ]
null
Ilya Gutkovskiy, Jan 25 2025
2025-01-25T17:16:40
oeisdata/seq/A380/A380499.seq
3a1fbba9d6f93fe812c327579ef07c5d
A380500
Table T(n,k) = phi(phi(prime(n)^k)), n >= 1, k >= 0, read by upwards antidiagonals, where phi = A000010.
[ "1", "1", "1", "1", "1", "1", "1", "2", "2", "2", "1", "2", "8", "6", "4", "1", "4", "12", "40", "18", "8", "1", "4", "40", "84", "200", "54", "16", "1", "8", "48", "440", "588", "1000", "162", "32", "1", "6", "128", "624", "4840", "4116", "5000", "486", "64", "1", "10", "108", "2176", "8112", "53240", "28812", "25000", "1458", "128", "1", "12", "220", "2052", "36992", "105456", "585640", "201684", "125000", "4374", "256" ]
[ "nonn", "easy", "tabl" ]
30
1
8
[ "A000010", "A000040", "A001248", "A008330", "A010554", "A046144", "A104039", "A246655", "A380500" ]
null
Michael De Vlieger, Feb 04 2025
2025-02-19T16:17:35
oeisdata/seq/A380/A380500.seq
865fa4da660c7b88ba8180683082ac83
A380501
Least positive integer v that belongs alongside its opposite -v to the minimal set of integers to add to the set {A377091(k), k = 0..A380938(n)} in order to obtain an integer interval.
[ "338", "365", "365", "393", "420", "420", "451", "543", "543", "543", "543", "543", "543", "543", "543", "543", "543", "543", "543", "543", "543", "543", "543", "543", "543", "543", "543", "543", "543", "543", "543", "543", "543", "543", "543", "543", "684", "684", "722", "724", "724", "760", "761", "1058", "1058", "4140", "5304", "5513", "5513", "5515" ]
[ "nonn" ]
24
1
1
[ "A377091", "A380501", "A380938", "A380939" ]
null
Rémy Sigrist, Feb 08 2025
2025-02-09T12:18:32
oeisdata/seq/A380/A380501.seq
c3d56154ef7e8f3f3eee17ecffe0055f
A380502
a(n) = (7*n^6 - 21*n^5 + 55*n^4 - 75*n^3 + 70*n^2 - 36*n + 8)/8.
[ "1", "1", "34", "370", "2179", "8791", "27586", "72514", "167245", "348949", "672706", "1216546", "2087119", "3425995", "5416594", "8291746", "12341881", "17923849", "25470370", "35500114", "48628411", "65578591", "87193954", "114450370", "148469509", "190532701", "242095426", "304802434", "380503495", "471269779", "579410866" ]
[ "nonn", "easy" ]
25
0
3
[ "A005448", "A075664", "A380353", "A380502" ]
null
Kelvin Voskuijl, Jan 25 2025
2025-02-09T18:09:52
oeisdata/seq/A380/A380502.seq
526a3077821e810694c55fbaae0a1233
A380503
Split A377091 into sublists consisting of runs of terms with the same sign. Sequence gives k's such that A377091(k) is the first term of those sublists whose terms (in absolute value) form an arithmetic progression with common difference 1.
[ "0", "1", "5", "10", "26", "37", "53", "82", "101", "122", "148", "197", "226", "257", "290", "325", "401", "442", "485", "530", "1093", "1157", "1370", "1526", "1602", "1682", "1765", "1850", "2116", "2210", "2306", "2403", "2501", "2602", "2708", "2920", "3026", "3137", "3365", "3482", "3601", "3722", "3970", "4097", "4226", "4357", "4493", "4762", "4901", "5042" ]
[ "nonn" ]
11
1
3
[ "A377091", "A379882", "A380417", "A380420", "A380503", "A380504", "A380505" ]
null
Paolo Xausa, Jan 25 2025
2025-01-26T20:40:28
oeisdata/seq/A380/A380503.seq
d44ec4bda2d13bd4ae9f249e9524bfad
A380504
Split A377091 into sublists consisting of runs of terms with the same sign. Sequence gives k's such that A377091(k) is the first term of those sublists whose terms (in absolute value) form an arithmetic progression with common difference -1.
[ "0", "3", "8", "1024", "1088", "1225", "1521", "1599", "2303", "2400", "2915", "8648", "8835", "9801", "10404", "12543", "12996", "13456", "14400", "14641", "15376", "17688", "17955", "19321", "20736", "40804", "47961", "54289", "55695", "56644", "58081", "60025", "60516", "64516", "65025", "66049", "66564", "71823", "72360", "75076", "77841" ]
[ "nonn" ]
6
1
2
[ "A377091", "A379882", "A380418", "A380422", "A380503", "A380504", "A380505" ]
null
Paolo Xausa, Jan 26 2025
2025-01-26T20:40:41
oeisdata/seq/A380/A380504.seq
8626758f60b7690faf717a884bd16420
A380505
Split A377091 into sublists consisting of runs of terms with the same sign. Sequence gives k's such that A377091(k) is the first term of those sublists whose terms form an arithmetic progression with common difference 1 or -1.
[ "0", "1", "3", "5", "8", "10", "26", "37", "53", "82", "101", "122", "148", "197", "226", "257", "290", "325", "401", "442", "485", "530", "1024", "1088", "1093", "1157", "1225", "1370", "1521", "1526", "1599", "1602", "1682", "1765", "1850", "2116", "2210", "2303", "2306", "2400", "2403", "2501", "2602", "2708", "2915", "2920", "3026", "3137", "3365", "3482" ]
[ "nonn" ]
7
1
3
[ "A377091", "A379882", "A380419", "A380423", "A380503", "A380504", "A380505" ]
null
Paolo Xausa, Jan 26 2025
2025-01-26T20:41:00
oeisdata/seq/A380/A380505.seq
4be75dceef36331cd1c2cd551e801df0
A380506
Smallest k such that A073734(k) is in A055932, where A073734 is the GCD of consecutive terms of the EKG sequence A064413.
[ "2", "3", "8", "968", "17", "11068", "3070", "58836", "50835", "403831", "20143", "18829", "868283", "458530", "245484", "46660", "199785", "5653022", "3603103", "477958", "2144637", "187759", "910595", "4181867", "1692138", "7454121", "10792662", "11232004", "36842536", "16878596", "1339550", "211463464", "3650538", "24922454" ]
[ "nonn" ]
29
1
1
[ "A002110", "A055932", "A064413", "A073734", "A380506", "A382222", "A382271" ]
null
Michael De Vlieger and Scott R. Shannon, Mar 23 2025
2025-03-25T15:03:34
oeisdata/seq/A380/A380506.seq
5d65b4884d8ac5de8e4d81cc47214e7c
A380507
Lexicographically earliest infinite sequence of positive integers such that for any n, consecutive occurrences of n are separated by a(n) terms and each subsequence enclosed by consecutive equal values is distinct.
[ "1", "2", "1", "3", "1", "3", "4", "3", "5", "3", "4", "6", "7", "8", "4", "6", "9", "7", "4", "6", "10", "11", "4", "6", "10", "12", "4", "6", "10", "13", "4", "6", "10", "14", "4", "6", "10", "13", "15", "6", "10", "16", "14", "6", "10", "13", "17", "6", "10", "18", "19", "6", "10", "13", "20", "6", "10", "18", "21", "6", "10", "13", "22", "6", "10", "18", "23", "6", "10", "13", "24", "6", "10", "18", "22" ]
[ "nonn" ]
9
1
2
[ "A363654", "A380278", "A380495", "A380507" ]
null
Neal Gersh Tolunsky, Jan 25 2025
2025-01-31T01:42:01
oeisdata/seq/A380/A380507.seq
3822acf5b21d88df2c0f8595344cea47
A380508
Lexicographically earliest sequence of positive integers such that for any n, consecutive occurrences of n are separated by a(n) distinct terms and each subsequence enclosed by consecutive equal values is distinct.
[ "1", "2", "1", "3", "1", "2", "4", "5", "2", "5", "6", "2", "4", "6", "2", "7", "4", "2", "8", "9", "2", "4", "7", "2", "10", "4", "2", "8", "7", "2", "4", "11", "2", "10", "4", "7", "8", "12", "4", "11", "7", "10", "4", "8", "13", "7", "4", "14", "10", "8", "4", "7", "11", "15", "4", "10", "7", "8", "4", "14", "11", "7", "4", "10", "8", "16", "4", "7", "14", "10", "4", "8", "7", "11", "4", "17", "10", "7", "4", "8", "14" ]
[ "nonn" ]
11
1
2
[ "A363654", "A380278", "A380495", "A380508" ]
null
Neal Gersh Tolunsky, Jan 26 2025
2025-01-31T04:29:18
oeisdata/seq/A380/A380508.seq
570486237949e8933b02444a4c6d8aba
A380509
Numbers of the form i+j+4ij for i,j >= 1 together with numbers of the form -i-j+4ij for i,j >= 2.
[ "6", "11", "12", "16", "19", "20", "21", "26", "29", "30", "31", "33", "36", "38", "40", "41", "42", "46", "47", "51", "52", "54", "55", "56", "61", "63", "65", "66", "68", "71", "72", "74", "75", "76", "81", "82", "83", "85", "86", "89", "90", "91", "92", "94", "96", "101", "103", "106", "107", "109", "110", "111", "116", "117", "118", "119", "120", "121", "123", "124", "126", "128", "129", "131", "132", "133" ]
[ "nonn" ]
33
1
1
[ "A054520", "A380140", "A380509", "A380549", "A380550", "A380572" ]
null
Davide Rotondo, Jan 26 2025
2025-01-31T04:23:45
oeisdata/seq/A380/A380509.seq
9216f271ff4dc484643d6129ba351393
A380510
Split A377091 into sublists consisting of runs of terms with the same sign. Then a(n) = 1 if sorted terms in the n-th sublist form an arithmetic progression with common difference 1, 0 otherwise.
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "1", "1", "0", "1", "1", "1", "1" ]
[ "nonn" ]
14
1
null
[ "A377091", "A379882", "A380417", "A380418", "A380419", "A380510" ]
null
Paolo Xausa, Jan 26 2025
2025-01-28T02:44:56
oeisdata/seq/A380/A380510.seq
a10b265443b4741b780777eba1a5efb3
A380511
Expansion of e.g.f. exp(x*G(x)^2) where G(x) = 1 + x*G(x)^3 is the g.f. of A001764.
[ "1", "1", "5", "55", "961", "23141", "711421", "26631235", "1175535425", "59786520841", "3442729157461", "221413508687471", "15730688410899265", "1223574846548300845", "103417508018836074701", "9437941200860641295611", "924934291227615821904001", "96881241931552168636182545", "10801002623361396194857667365" ]
[ "nonn" ]
22
0
3
[ "A001764", "A006013", "A080893", "A082579", "A251568", "A251569", "A370054", "A380511", "A380512", "A380514", "A380515", "A382058" ]
null
Seiichi Manyama, Jan 26 2025
2025-03-15T09:43:28
oeisdata/seq/A380/A380511.seq
6382e8f81f27731de774cc826cfb9583