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2
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348
keywords
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score
int64
1
2.31k
offset_a
int64
-14,827
666,262,453B
offset_b
int64
0
635M
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cross_references
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1999-12-11 03:00:00
2025-04-28 00:58:08
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A360701
Decimal expansion of arccsc(Pi).
[ "3", "2", "3", "9", "4", "6", "1", "0", "6", "9", "3", "1", "9", "8", "0", "7", "1", "9", "9", "8", "0", "9", "5", "2", "8", "3", "0", "6", "2", "8", "7", "7", "3", "8", "3", "5", "6", "7", "2", "7", "5", "6", "1", "2", "5", "4", "7", "2", "1", "2", "1", "3", "2", "5", "5", "3", "7", "0", "6", "1", "3", "7", "8", "2", "5", "9", "5", "8", "4", "2", "2", "9", "1", "8", "0", "9", "0", "2", "8", "9", "0", "1", "9", "2", "3", "3", "8", "0", "5", "8", "9", "3", "8", "9", "5", "4", "3", "4", "3", "7", "8", "6", "2", "7", "1" ]
[ "cons", "nonn" ]
8
0
1
[ "A232272", "A232273", "A360700", "A360701" ]
null
Wolfe Padawer, Feb 16 2023
2023-03-04T09:00:53
oeisdata/seq/A360/A360701.seq
21dab33501e4be3e3382ced4eef1c096
A360702
Number of sets of 2n words of length 2n over binary alphabet where each letter occurs 2n^2 times.
[ "1", "2", "394", "10247250", "41192135957378", "26708408307353573010350", "3044454667114388718324075325130428", "65233919825974729088553743803268484284650384722", "275236371094876077407367002758415347571615535684540339803854604" ]
[ "nonn" ]
22
0
2
[ "A001105", "A360693", "A360702" ]
null
Alois P. Heinz, Feb 16 2023
2023-02-19T02:40:17
oeisdata/seq/A360/A360702.seq
47831e26a57492a35979ca35a50e35ef
A360703
Starting from 1, successively take the smallest "Choix de Bruxelles" with factor 3 which is not already in the sequence.
[ "1", "3", "9", "27", "67", "187", "129", "43", "41", "121", "17", "37", "97", "277", "677", "1877", "1297", "199", "133", "111", "113", "119", "139", "339", "313", "311", "331", "131", "191", "193", "393", "333", "399", "999", "933", "911", "913", "919", "319", "357", "157", "57", "19", "13", "11", "31", "33", "39", "99", "93", "91", "271", "273", "279", "679", "673", "671", "1871", "1291", "197", "137", "117", "151", "51", "53", "59", "159", "153" ]
[ "nonn", "base" ]
26
0
2
[ "A323286", "A358708", "A360190", "A360703" ]
null
Alon Vinkler, Feb 16 2023
2025-01-09T13:04:40
oeisdata/seq/A360/A360703.seq
7226029b4d8f45ed72f81a477194a64c
A360704
Expansion of Sum_{k>=0} (x * (1 + 2^k * x))^k.
[ "1", "1", "3", "9", "41", "257", "2209", "27009", "455553", "10831873", "360452609", "16786663425", "1102243190785", "101146710556673", "13109796072955905", "2379217548538511361", "609386444958743363585", "219178211386515281412097", "111098724276069341895720961", "79284929294467154275606200321" ]
[ "nonn" ]
10
0
3
[ "A000684", "A117402", "A360592", "A360696", "A360704", "A360705" ]
null
Seiichi Manyama, Feb 17 2023
2023-02-17T03:19:41
oeisdata/seq/A360/A360704.seq
87d7ab5798725def08e368c8f0214ac1
A360705
Expansion of Sum_{k>=0} (x * (1 + (-1)^k * x))^k.
[ "1", "1", "0", "3", "-1", "8", "1", "21", "0", "55", "-1", "144", "1", "377", "0", "987", "-1", "2584", "1", "6765", "0", "17711", "-1", "46368", "1", "121393", "0", "317811", "-1", "832040", "1", "2178309", "0", "5702887", "-1", "14930352", "1", "39088169", "0", "102334155", "-1", "267914296", "1", "701408733", "0", "1836311903", "-1", "4807526976", "1" ]
[ "sign", "easy" ]
25
0
4
[ "A000045", "A001906", "A057078", "A360592", "A360696", "A360704", "A360705" ]
null
Seiichi Manyama, Feb 17 2023
2023-03-12T10:34:03
oeisdata/seq/A360/A360705.seq
42ea5f0856de8183e5b4da215af781a5
A360706
a(n) is the least positive number not yet used such that its binary representation has either all or none of its 1-bits in common with the XOR of a(1) to a(n-1).
[ "1", "2", "3", "4", "8", "12", "5", "10", "6", "9", "7", "16", "17", "24", "14", "11", "18", "20", "13", "15", "19", "32", "36", "21", "25", "26", "22", "23", "27", "33", "37", "28", "34", "30", "29", "40", "42", "31", "64", "96", "35", "68", "38", "44", "41", "43", "39", "48", "56", "45", "65", "66", "46", "47", "67", "80", "52", "49", "57", "50", "82", "69", "97", "51", "53", "60", "54", "55", "58", "72", "73", "59", "61", "76", "70", "71", "74" ]
[ "nonn", "base" ]
51
1
2
[ "A000120", "A116624", "A269868", "A330647", "A360363", "A360706", "A375856" ]
null
Thomas Scheuerle, Feb 17 2023
2024-09-01T16:49:34
oeisdata/seq/A360/A360706.seq
97e4a702591e4b705523b1d82ba2bd58
A360707
G.f.: Sum_{k>=0} (1 + k*x)^k * x^(3*k).
[ "1", "0", "0", "1", "1", "0", "1", "4", "4", "1", "9", "27", "28", "16", "96", "257", "281", "250", "1251", "3161", "3665", "4321", "19489", "47685", "58662", "84099", "354739", "852216", "1110344", "1837924", "7401269", "17604002", "24221890", "44761045", "174287005", "412627144", "597640105", "1204831674", "4574415066", "10818841343" ]
[ "nonn" ]
11
0
8
[ "A360592", "A360699", "A360707", "A360747" ]
null
Vaclav Kotesovec, Feb 17 2023
2023-02-20T03:15:56
oeisdata/seq/A360/A360707.seq
6ae5689574fec2820f86808e71a417cd
A360708
Expansion of Sum_{k>=0} (x^2 / (1 - k*x))^k.
[ "1", "0", "1", "1", "2", "5", "14", "42", "136", "479", "1825", "7433", "32053", "145608", "695081", "3479117", "18209842", "99373513", "563920590", "3320674902", "20255823092", "127799984935", "832807892861", "5597481205009", "38753768384761", "276057156622776", "2021100095469577", "15193591060371577" ]
[ "nonn" ]
17
0
5
[ "A000248", "A080108", "A360699", "A360708", "A360709" ]
null
Seiichi Manyama, Feb 17 2023
2023-02-20T07:36:28
oeisdata/seq/A360/A360708.seq
fe8c9a44c48440b3844b4abca1ebb3a8
A360709
Expansion of Sum_{k>=0} (x^3 / (1 - k*x))^k.
[ "1", "0", "0", "1", "1", "1", "2", "5", "13", "34", "90", "247", "720", "2256", "7568", "26814", "98982", "377541", "1484254", "6021789", "25271173", "109850447", "494355359", "2298362532", "11008133629", "54175202125", "273460921605", "1414449612648", "7494262602464", "40669492399396" ]
[ "nonn" ]
11
0
7
[ "A078012", "A080108", "A360707", "A360708", "A360709" ]
null
Seiichi Manyama, Feb 17 2023
2023-02-17T12:16:00
oeisdata/seq/A360/A360709.seq
73f4f08d80f9b08392c33633d552396d
A360710
Multiplicative with a(p^k) = 1 or -1 so as to minimize abs(Sum_{m = 1..p^k} a(m)); in case of a tie, a(p^k) = a(p^k-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", "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" ]
[ "sign", "mult" ]
10
1
null
[ "A360710", "A360711" ]
null
Rémy Sigrist, Feb 17 2023
2023-02-19T12:31:31
oeisdata/seq/A360/A360710.seq
9c818375e1a94482d8ef5e34aac178e7
A360711
Partial sums of A360710.
[ "0", "1", "0", "-1", "0", "1", "2", "1", "0", "-1", "-2", "-1", "-2", "-1", "0", "-1", "0", "1", "2", "1", "2", "3", "2", "1", "2", "1", "0", "-1", "-2", "-1", "0", "1", "0", "-1", "-2", "-3", "-4", "-3", "-2", "-3", "-4", "-3", "-4", "-3", "-2", "-3", "-2", "-1", "-2", "-1", "0", "-1", "0", "1", "2", "3", "4", "5", "4", "3", "2", "1", "0", "1", "0", "1", "2", "1", "2", "3", "4", "3", "4", "3", "2", "3", "2", "1" ]
[ "sign", "look" ]
12
0
7
[ "A360710", "A360711" ]
null
Rémy Sigrist, Feb 17 2023
2023-02-19T11:16:17
oeisdata/seq/A360/A360711.seq
c4d28031b754d426ffe0a842d09d7cba
A360712
Expansion of Sum_{k>0} (k * x * (1 + k*x^k))^k.
[ "1", "5", "27", "272", "3125", "46915", "823543", "16781312", "387421218", "10000078125", "285311670611", "8916102153177", "302875106592253", "11112006865911623", "437893890381640625", "18446744074783358976", "827240261886336764177", "39346408075327943829273" ]
[ "nonn" ]
25
1
2
[ "A217668", "A327249", "A338693", "A359700", "A360618", "A360712" ]
null
Seiichi Manyama, Feb 17 2023
2023-08-09T00:52:04
oeisdata/seq/A360/A360712.seq
98dcbe706ef2b085587a5e24849ae41f
A360713
Sum of all prime encoded perfect partitions of n.
[ "1", "2", "4", "14", "16", "70", "64", "280", "356", "850", "1024", "4630", "4096", "10738", "20820", "47264", "65536", "176712", "262144", "643214", "1129572", "2246994", "4194304", "9716880", "17011472", "34785250", "68859688", "139829626", "268435456", "560518826", "1073741824", "2192136576", "4335013860", "8679894658" ]
[ "nonn" ]
24
0
2
[ "A002033", "A215366", "A258119", "A360713", "A360791" ]
null
Alois P. Heinz, Feb 21 2023
2023-11-21T08:40:33
oeisdata/seq/A360/A360713.seq
ff516750b8f97d906f8f2a7cca1103e6
A360714
Number of sets of nonempty integer partitions with a total of n parts and total sum of 2n.
[ "1", "1", "3", "10", "30", "94", "287", "854", "2501", "7222", "20502", "57412", "158678", "433204", "1169274", "3122747", "8256669", "21627238", "56150750", "144570308", "369288160", "936246670", "2356750215", "5892267672", "14636329019", "36131588682", "88667056302", "216353770900", "525040244748", "1267473283199" ]
[ "nonn" ]
11
0
3
[ "A360468", "A360714", "A360742" ]
null
Alois P. Heinz, Feb 17 2023
2023-02-18T16:01:26
oeisdata/seq/A360/A360714.seq
e64e63be46cc94b6a14c0e72d430615d
A360715
Number of self-avoiding paths with nodes chosen among n given points on a circle; one-node paths are allowed.
[ "1", "3", "9", "30", "105", "369", "1281", "4380", "14769", "49215", "162393", "531450", "1727193", "5580141", "17936145", "57395640", "182948577", "581130747", "1840247337", "5811307350", "18305618121", "57531942633", "180441092769", "564859072980", "1765184603025", "5507375961399", "17157594341241", "53379182394930", "165856745298489", "514727830236645" ]
[ "nonn", "easy" ]
23
1
2
[ "A001792", "A261064", "A360715" ]
null
Ivaylo Kortezov, Feb 18 2023
2023-03-04T20:36:52
oeisdata/seq/A360/A360715.seq
b2308477c8e0078f724dbda8c7cac490
A360716
Number of unordered pairs of self-avoiding paths whose sets of nodes are disjoint subsets of a set of n points on a circle; one-node paths are not allowed.
[ "0", "0", "0", "3", "45", "435", "3465", "24794", "165942", "1061730", "6578550", "39796053", "236309931", "1382504669", "7989938775", "45704622660", "259155482652", "1458298435572", "8151155034300", "45290328792695", "250308998693145", "1376766613411959", "7539656755416885", "41126122248463038", "223513887538508850", "1210707873300202550", "6537847299012919890" ]
[ "nonn", "easy" ]
22
1
4
[ "A261064", "A332426", "A360716" ]
null
Ivaylo Kortezov, Feb 18 2023
2023-03-04T20:36:20
oeisdata/seq/A360/A360716.seq
2fb4fe21f52b601832acf6133fb5db6d
A360717
Number of unordered pairs of self-avoiding paths whose sets of nodes are disjoint subsets of a set of n points on a circle; one-node paths are allowed.
[ "0", "1", "6", "33", "185", "1050", "6027", "35014", "205326", "1209375", "7119860", "41744703", "243218703", "1406685280", "8073640785", "45991600860", "260131208396", "1461591509805", "8162196518322", "45327133739245", "250431036147285", "1377169337010390", "7540979990097191", "41130452834689218", "223528009015333050", "1210753768099880875", "6537995998163877312" ]
[ "nonn" ]
22
1
3
[ "A360715", "A360716", "A360717" ]
null
Ivaylo Kortezov, Feb 18 2023
2023-03-06T13:49:13
oeisdata/seq/A360/A360717.seq
464cbcb42a2314de4b25976732cdcc7a
A360718
Number of idempotent Boolean relation matrices on [n] that have no proper power primitive.
[ "1", "2", "9", "52", "459", "5526", "91161", "2039024", "62264215", "2618031658", "153147765333", "12544274587956", "1443661355799075", "233590364506712318", "53152637809972391281", "17010099259539378971368", "7660283773351147860024879", "4856904906875123474086041426" ]
[ "nonn" ]
41
0
2
[ "A001831", "A002031", "A121337", "A360718", "A360743" ]
null
Geoffrey Critzer, Feb 24 2023
2024-02-15T02:43:58
oeisdata/seq/A360/A360718.seq
3cb71d929099d3963400f1e349784206
A360719
a(n) is the largest k < A126706(n) such that rad(k) = rad(A126706(n)), where rad(n) = A007947(n).
[ "6", "12", "10", "18", "14", "24", "20", "22", "15", "36", "40", "26", "48", "28", "30", "21", "34", "54", "45", "38", "50", "42", "44", "60", "46", "72", "56", "33", "80", "52", "96", "98", "58", "39", "90", "62", "84", "66", "75", "68", "70", "108", "63", "74", "120", "76", "51", "78", "100", "144", "82", "126", "57", "86", "35", "88", "150", "92", "94", "147", "162", "112", "132", "160", "102", "69", "104", "106", "192", "110", "196", "135" ]
[ "nonn" ]
16
1
1
[ "A007947", "A126706", "A360529", "A360719" ]
null
Michael De Vlieger, May 01 2023
2023-05-19T04:24:32
oeisdata/seq/A360/A360719.seq
88010c25abbf9d3f42ded6b5581aafe6
A360720
a(n) is the sum of unitary divisors of n that are powerful (A001694).
[ "1", "1", "1", "5", "1", "1", "1", "9", "10", "1", "1", "5", "1", "1", "1", "17", "1", "10", "1", "5", "1", "1", "1", "9", "26", "1", "28", "5", "1", "1", "1", "33", "1", "1", "1", "50", "1", "1", "1", "9", "1", "1", "1", "5", "10", "1", "1", "17", "50", "26", "1", "5", "1", "28", "1", "9", "1", "1", "1", "5", "1", "1", "10", "65", "1", "1", "1", "5", "1", "1", "1", "90", "1", "1", "26", "5", "1", "1", "1", "17", "82" ]
[ "nonn", "mult", "easy" ]
30
1
4
[ "A001694", "A004709", "A034444", "A034448", "A057521", "A077610", "A183097", "A323308", "A360720", "A360722" ]
null
Amiram Eldar, Feb 18 2023
2025-01-25T06:57:42
oeisdata/seq/A360/A360720.seq
8f7fa33b25ee96783f96de7e73816885
A360721
a(n) is the number of infinitary divisors of n that are powerful (A001694).
[ "1", "1", "1", "2", "1", "1", "1", "3", "2", "1", "1", "2", "1", "1", "1", "2", "1", "2", "1", "2", "1", "1", "1", "3", "2", "1", "3", "2", "1", "1", "1", "3", "1", "1", "1", "4", "1", "1", "1", "3", "1", "1", "1", "2", "2", "1", "1", "2", "2", "2", "1", "2", "1", "3", "1", "3", "1", "1", "1", "2", "1", "1", "2", "4", "1", "1", "1", "2", "1", "1", "1", "6", "1", "1", "2", "2", "1", "1", "1", "2", "2", "1", "1", "2", "1", "1", "1" ]
[ "nonn", "mult", "easy" ]
9
1
4
[ "A000120", "A001694", "A005361", "A037445", "A077609", "A323308", "A360721", "A360723" ]
null
Amiram Eldar, Feb 18 2023
2023-02-26T03:27:34
oeisdata/seq/A360/A360721.seq
c17fe907dcf791688dac8f229b55c315
A360722
a(n) is the sum of infinitary divisors of n that are powerful (A001694).
[ "1", "1", "1", "5", "1", "1", "1", "13", "10", "1", "1", "5", "1", "1", "1", "17", "1", "10", "1", "5", "1", "1", "1", "13", "26", "1", "37", "5", "1", "1", "1", "49", "1", "1", "1", "50", "1", "1", "1", "13", "1", "1", "1", "5", "10", "1", "1", "17", "50", "26", "1", "5", "1", "37", "1", "13", "1", "1", "1", "5", "1", "1", "10", "85", "1", "1", "1", "5", "1", "1", "1", "130", "1", "1", "26", "5", "1", "1", "1", "17" ]
[ "nonn", "mult", "easy" ]
11
1
4
[ "A001694", "A049417", "A077609", "A077610", "A183097", "A360721", "A360722", "A360723" ]
null
Amiram Eldar, Feb 18 2023
2023-02-26T03:27:31
oeisdata/seq/A360/A360722.seq
5e64d341321a647d0f0bc8e0b40a66ac
A360723
Numbers that have at least one exponent in their canonical prime factorization that is neither 2 nor of the form 2^k-1, k>=1.
[ "16", "32", "48", "64", "80", "81", "96", "112", "144", "160", "162", "176", "192", "208", "224", "240", "243", "256", "272", "288", "304", "320", "324", "336", "352", "368", "400", "405", "416", "432", "448", "464", "480", "486", "496", "512", "528", "544", "560", "567", "576", "592", "608", "624", "625", "648", "656", "672", "688", "704", "720", "729", "736", "752" ]
[ "nonn", "easy" ]
24
1
1
[ "A000225", "A000290", "A001694", "A005361", "A077609", "A360721", "A360723" ]
null
Amiram Eldar, Feb 18 2023
2023-05-27T05:18:51
oeisdata/seq/A360/A360723.seq
78f3adc7309d4e50206f6776789de5a0
A360724
Hajnal's recurrence: a(2n) = a(n) + 3*a(n-1); a(2n+1) = 3*a(n) + a(n-1), with initial values a(0) = 0, a(1) = 1.
[ "0", "1", "1", "3", "4", "4", "6", "10", "13", "15", "16", "16", "18", "22", "28", "36", "43", "49", "54", "58", "61", "63", "64", "64", "66", "70", "76", "84", "94", "106", "120", "136", "151", "165", "178", "190", "201", "211", "220", "228", "235", "241", "246", "250", "253", "255", "256", "256", "258", "262", "268", "276", "286", "298", "312", "328", "346", "366", "388" ]
[ "nonn", "look" ]
22
0
4
null
null
Jeffrey Shallit, Feb 18 2023
2023-02-24T20:47:25
oeisdata/seq/A360/A360724.seq
b6888c3440cbb25cbb4a319b41453eb6
A360725
Number of ways to tile an n X n square using oblongs with distinct height x width dimensions.
[ "0", "0", "4", "36", "1056", "31052", "1473944", "87469884" ]
[ "nonn", "more" ]
4
1
3
[ "A004003", "A065072", "A099390", "A182275", "A360256", "A360498", "A360499", "A360725" ]
null
Scott R. Shannon, Feb 18 2023
2023-02-18T08:08:43
oeisdata/seq/A360/A360725.seq
791137a6230fe7b0ae22b276a2e49cd8
A360726
Expansion of Sum_{k>0} (k * x * (1 + x^k))^k.
[ "1", "5", "27", "264", "3125", "46741", "823543", "16778240", "387420570", "10000015625", "285311670611", "8916100729755", "302875106592253", "11112006831322817", "437893890380890625", "18446744073843770368", "827240261886336764177", "39346408075300025059665" ]
[ "nonn" ]
19
1
2
[ "A360611", "A360712", "A360726", "A360727", "A360728", "A360732" ]
null
Seiichi Manyama, Feb 18 2023
2023-08-02T02:00:24
oeisdata/seq/A360/A360726.seq
9a1fcdf5716398498f9230155e029961
A360727
Expansion of Sum_{k>=0} (k * x * (1 + x^2))^k.
[ "1", "1", "4", "28", "264", "3206", "47684", "839249", "17058688", "393216567", "10134918592", "288815780665", "9016571143680", "306027510946208", "11219450971161024", "441846991480590475", "18602901833071633792", "833832341625621777368", "39642569136740054367808" ]
[ "nonn" ]
17
0
3
[ "A360611", "A360727", "A360728", "A360730" ]
null
Seiichi Manyama, Feb 18 2023
2023-02-18T19:00:40
oeisdata/seq/A360/A360727.seq
a2dd7cc2519d2285298da41c3e97950d
A360728
Expansion of Sum_{k>=0} (k * x * (1 + x^3))^k.
[ "1", "1", "4", "27", "257", "3133", "46737", "824567", "16792845", "387700506", "10005766337", "285445919589", "8919587932524", "302975123887680", "11115145723728035", "438000897534309171", "18450681900124075166", "827395845674975999727", "39352977072147424071861" ]
[ "nonn" ]
13
0
3
[ "A360611", "A360727", "A360728", "A360731" ]
null
Seiichi Manyama, Feb 18 2023
2023-02-18T19:00:19
oeisdata/seq/A360/A360728.seq
b1be0acd0e2e69e273fe80e7cc5dbd01
A360729
a(n) is the number of prime factors of the n-th powerful number (counted with repetition).
[ "0", "2", "3", "2", "4", "2", "3", "5", "4", "2", "6", "5", "4", "4", "5", "2", "3", "7", "6", "2", "4", "5", "6", "4", "5", "8", "7", "2", "6", "3", "2", "5", "6", "7", "4", "4", "5", "9", "2", "8", "4", "7", "5", "4", "6", "6", "7", "2", "8", "6", "2", "5", "7", "6", "10", "4", "5", "9", "4", "4", "8", "5", "3", "5", "2", "5", "4", "4", "7", "8", "2", "9", "6", "7", "2", "6", "8", "7", "6", "11", "4", "7", "3", "2", "10", "5" ]
[ "nonn" ]
19
1
2
[ "A001222", "A001694", "A072047", "A076399", "A083342", "A090699", "A360729" ]
null
Amiram Eldar, Feb 18 2023
2024-09-21T14:48:03
oeisdata/seq/A360/A360729.seq
d1b02632c97cbb68f1336f1fcfe4554a
A360730
Expansion of Sum_{k>=0} (k * x * (1 + k*x^2))^k.
[ "1", "1", "4", "28", "272", "3368", "50768", "902397", "18481408", "428556075", "11099001600", "317544062217", "9946366838784", "338537433281448", "12441407233436672", "491002325860132371", "20710640842719301632", "929821866165431838038", "44270378887441746923520" ]
[ "nonn" ]
12
0
3
[ "A360618", "A360730", "A360731" ]
null
Seiichi Manyama, Feb 18 2023
2023-02-18T19:00:30
oeisdata/seq/A360/A360730.seq
ca1cfa9e853a8c7242a140d0b1d8b705
A360731
Expansion of Sum_{k>=0} (k * x * (1 + k*x^3))^k.
[ "1", "1", "4", "27", "257", "3141", "46899", "827639", "16855357", "389100834", "10040378183", "286386193685", "8947506702834", "303875954083536", "11146559606379269", "439178938765108083", "18497974976610341624", "829420114454360154295", "39445018962975879216867" ]
[ "nonn" ]
12
0
3
[ "A360618", "A360730", "A360731" ]
null
Seiichi Manyama, Feb 18 2023
2023-02-18T19:57:52
oeisdata/seq/A360/A360731.seq
f79e078a533d5218bb4826e18ea2598f
A360732
Expansion of Sum_{k>0} (k * x * (1 + (k * x)^k))^k.
[ "1", "5", "27", "288", "3125", "48907", "823543", "17039360", "387479538", "10048828125", "285311670611", "8929262337009", "302875106592253", "11116754387067959", "437894195556640625", "18448995890703106048", "827240261886336764177", "39347760450413560593753" ]
[ "nonn" ]
16
1
2
[ "A360712", "A360726", "A360732" ]
null
Seiichi Manyama, Feb 18 2023
2023-08-09T00:51:19
oeisdata/seq/A360/A360732.seq
57d3061d772ffb5af30d65cd2a3087b4
A360733
Expansion of Sum_{k>0} (x * (1 + (k * x)^k))^k.
[ "1", "2", "1", "9", "1", "98", "1", "1025", "2188", "15626", "1", "692836", "1", "5764802", "97656251", "201326593", "1", "36138519442", "1", "409470748547", "14242684529830", "3138428376722", "1", "10019491686645761", "476837158203126", "3937376385699290", "5403406870691968357", "19704673338472752470", "1" ]
[ "nonn" ]
19
1
2
[ "A327249", "A360732", "A360733" ]
null
Seiichi Manyama, Feb 18 2023
2023-08-09T00:51:47
oeisdata/seq/A360/A360733.seq
9dedee618de84a9f36e8f3de7eef2a4d
A360734
The number of regions into which the plane is divided by a hypotrochoid with parameters R = d = prime(n+1) and r = prime(n).
[ "2", "7", "9", "35", "15", "53", "21", "71", "147", "33", "187", "125", "45", "143", "267", "297", "63", "337", "215", "75", "397", "251", "447", "681", "305", "105", "323", "111", "341", "1653", "395", "687", "141", "1343", "153", "787", "817", "503", "867", "897", "183", "1721", "195", "593", "201", "2323", "2455", "683", "231", "701", "1197" ]
[ "nonn" ]
20
1
1
[ "A000040", "A360734" ]
null
Nicolay Avilov, Feb 18 2023
2023-07-20T07:20:18
oeisdata/seq/A360/A360734.seq
35885474ad995c9d9a6d162845144924
A360735
Even integers d such that the longest possible arithmetic progression (AP) of primes with common difference d has only two elements.
[ "16", "22", "26", "32", "44", "46", "52", "56", "58", "62", "70", "74", "76", "82", "86", "88", "92", "100", "106", "112", "116", "118", "122", "128", "130", "136", "140", "142", "146", "148", "152", "158", "160", "166", "170", "172", "176", "182", "184", "194", "196", "200", "202", "206", "212", "214", "218", "224", "226", "232", "236", "242", "244", "250", "254", "256", "262", "266", "268" ]
[ "nonn" ]
31
1
1
[ "A040976", "A047235", "A123556", "A206037", "A342309", "A359408", "A360735" ]
null
Bernard Schott, Feb 19 2023
2023-03-03T16:52:34
oeisdata/seq/A360/A360735.seq
ae10a767544f1de9468239348650c20d
A360736
Number of prime divisors of A007942(n) = decimal concatenation of sequence (n, n-1, ..., 2, 1, 2, ..., n-1, n) counted with multiplicity.
[ "0", "3", "3", "2", "5", "8", "3", "4", "3", "3", "3", "5", "1", "4", "6", "3", "2", "3", "4", "11", "4", "8", "2", "4", "5", "6", "5", "9", "5", "6", "6", "4", "5", "7", "4", "8", "8", "5", "7", "7", "3", "3", "7", "9", "7", "7", "10", "8", "6", "7", "7", "10", "5", "5" ]
[ "nonn", "base", "more" ]
26
1
2
[ "A001222", "A007942", "A110760", "A360736", "A361624" ]
null
Bernard Schott, Mar 18 2023
2023-03-23T07:58:00
oeisdata/seq/A360/A360736.seq
8a70720e47b9d095f6ce40ac2a3726c4
A360737
Analog of the Moser-Newman sum sequence A005599, but counting 0's (instead of 1's) in the binary representation of 3*n.
[ "0", "1", "2", "1", "2", "3", "4", "3", "4", "3", "2", "1", "2", "3", "4", "3", "4", "5", "6", "7", "8", "9", "10", "9", "10", "9", "8", "7", "8", "9", "10", "9", "10", "9", "8", "7", "6", "5", "4", "3", "4", "3", "2", "1", "2", "3", "4", "3", "4", "5", "6", "7", "8", "9", "10", "9", "10", "9", "8", "7", "8", "9", "10", "9", "10", "11", "12", "13", "14", "15", "16", "17", "16", "17", "18", "19", "20", "21", "22" ]
[ "nonn" ]
18
0
3
[ "A005599", "A080791", "A360737" ]
null
Jeffrey Shallit, Feb 18 2023
2023-02-21T07:32:17
oeisdata/seq/A360/A360737.seq
2e153fb83a61f398558a933ca8c2931b
A360738
a(n) = A084740(n) - 1.
[ "1", "1", "2", "1", "2", "1", "4", "2", "-1", "1", "16", "1", "4", "2", "2", "1", "2", "1", "18", "2", "2", "1", "4", "2", "-1", "6", "2", "1", "4", "1", "6", "-1", "2", "12", "312", "1", "12", "2", "348", "1", "2", "1", "4", "4", "18", "1", "126", "18", "-1", "2", "4228", "1", "10", "2", "16", "6", "2", "1", "2", "1", "6", "2", "4", "-1", "18", "1", "18", "4", "2", "1", "2", "1", "4", "4", "2", "40", "2", "1", "4", "2", "-1", "1", "4", "16", "4", "10", "6", "1", "2", "2", "4420" ]
[ "sign" ]
36
1
3
[ "A084740", "A360738" ]
null
Ya-Ping Lu, Feb 18 2023
2023-03-05T11:37:11
oeisdata/seq/A360/A360738.seq
df1f1471d174c5ad1cbc4b492f580204
A360739
Semiprimes of the form k^2 + 2.
[ "6", "38", "51", "123", "146", "291", "326", "731", "843", "1227", "1371", "1766", "1851", "2306", "2603", "2811", "2918", "3027", "3602", "4227", "4358", "4763", "5186", "5331", "5627", "6243", "6891", "7058", "7571", "8102", "8651", "9411", "13227", "14163", "15627", "17426", "17691", "18227", "18771", "19883", "20738", "22502", "23411", "24027" ]
[ "nonn", "easy" ]
20
1
1
[ "A001358", "A059100", "A085722", "A144255", "A242330", "A360739" ]
null
Elmo R. Oliveira, Feb 18 2023
2023-03-13T16:23:49
oeisdata/seq/A360/A360739.seq
73fc46ae831d94341d3521367a997f84
A360740
Semiprimes of the form k^2 + 3.
[ "4", "39", "259", "327", "403", "579", "679", "1027", "1159", "1299", "1603", "1939", "2119", "2307", "3139", "3603", "4359", "4627", "6087", "6403", "7747", "9607", "10003", "10407", "10819", "11667", "13459", "13927", "14403", "16387", "18499", "21907", "23107", "26899", "28903", "30279", "30979", "33127", "35347", "36103", "36867", "38419" ]
[ "nonn", "easy" ]
29
1
1
[ "A001358", "A085722", "A117950", "A144255", "A242330", "A242331", "A360740" ]
null
Elmo R. Oliveira, Feb 18 2023
2023-03-13T16:23:27
oeisdata/seq/A360/A360740.seq
37eca18d899921ad783fa0d0b5417d81
A360741
Semiprimes of the form k^2 + 4.
[ "4", "85", "365", "445", "533", "629", "965", "1685", "1853", "2605", "2813", "3029", "3973", "4765", "5045", "5629", "5933", "6245", "6893", "8285", "8653", "11029", "11453", "11885", "12773", "14165", "15133", "16645", "17165", "17693", "20453", "21029", "22205", "22805", "23413", "24653", "27229", "29245", "29933", "30629", "32765", "34229" ]
[ "nonn", "easy" ]
22
1
1
[ "A001358", "A085722", "A087475", "A144255", "A242330", "A242331", "A242332", "A360741" ]
null
Elmo R. Oliveira, Feb 18 2023
2023-03-13T16:22:25
oeisdata/seq/A360/A360741.seq
a9fcf0eeda55d66f74bb9439056db083
A360742
Number T(n,k) of sets of nonempty integer partitions with a total of k parts and total sum of n; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
[ "1", "0", "1", "0", "1", "1", "0", "1", "2", "2", "0", "1", "3", "3", "2", "0", "1", "4", "6", "5", "3", "0", "1", "5", "10", "10", "7", "4", "0", "1", "6", "14", "19", "16", "10", "5", "0", "1", "7", "19", "30", "32", "24", "14", "6", "0", "1", "8", "26", "46", "57", "52", "35", "19", "8", "0", "1", "9", "32", "67", "94", "97", "79", "50", "25", "10", "0", "1", "10", "40", "93", "147", "172", "157", "117", "69", "33", "12" ]
[ "nonn", "tabl" ]
28
0
9
[ "A000007", "A000009", "A000041", "A001477", "A036469", "A055884", "A057427", "A261049", "A330463", "A360714", "A360742" ]
null
Alois P. Heinz, Feb 18 2023
2023-11-15T08:09:30
oeisdata/seq/A360/A360742.seq
a8c62b108b1ab3bfc7a872b9d6fc8d8a
A360743
Number of idempotent binary relation matrices E on [n] such that E contains an identity matrix of order n-1 and (E - I_n)^2 = 0.
[ "1", "2", "9", "52", "435", "5046", "81501", "1823144", "56572263", "2435930410", "145888123953", "12173595399516", "1418664206897691", "231298954644947294", "52860840028599821445", "16957903154151836822608", "7647128139328190245443279", "4852236755345544324027858258" ]
[ "nonn" ]
30
0
2
[ "A001831", "A121337", "A360743" ]
null
Geoffrey Critzer, Feb 18 2023
2023-02-27T17:23:52
oeisdata/seq/A360/A360743.seq
6c6f7d6e25a5c0bd6bd57b638ad11fd5
A360744
a(n) is the maximum number of locations 1..n-1 which can be reached starting from some location s, where jumps from location i to i +- a(i) are permitted (within 1..n-1); a(1)=1. See example.
[ "1", "1", "2", "3", "4", "5", "5", "6", "6", "7", "7", "9", "10", "10", "10", "11", "11", "13", "14", "14", "14", "15", "15", "15", "15", "21", "21", "21", "22", "22", "22", "23", "23", "23", "23", "24", "24", "26", "27", "28", "29", "29", "29", "29", "29", "29", "29", "29", "29", "32", "32", "32", "32", "33", "33", "35", "35", "41", "42", "42", "42", "43", "43", "43", "44", "44", "45", "45", "46", "46", "46", "46", "46", "46", "47", "47", "49", "49", "51", "51", "51" ]
[ "nonn" ]
58
1
3
[ "A358838", "A359005", "A359008", "A360593", "A360744", "A360745", "A360746", "A361383", "A362248" ]
null
Neal Gersh Tolunsky, Feb 18 2023
2023-05-26T11:30:27
oeisdata/seq/A360/A360744.seq
450be929156f3d68c62982fc5875d5cc
A360745
a(n) is the maximum number of locations 1..n-1 which can be reached starting from a(1)=1, where jumps from location i to i +- a(i) are permitted (within 1..n-1). See example.
[ "1", "1", "2", "3", "3", "4", "4", "4", "7", "7", "7", "8", "9", "9", "9", "9", "9", "9", "12", "12", "13", "13", "13", "13", "13", "14", "14", "17", "17", "17", "17", "17", "24", "24", "24", "25", "25", "26", "27", "27", "28", "29", "29", "29", "29", "29", "29", "29", "29", "30", "30", "30", "30", "30", "30", "30", "30", "30", "30", "33", "33", "33", "34", "34", "37", "37", "37", "38", "38", "48", "48", "48", "48", "48", "49", "50", "51", "52", "53", "53", "53" ]
[ "nonn" ]
39
1
3
[ "A358838", "A359005", "A359008", "A360593", "A360744", "A360745", "A360746", "A361383" ]
null
Neal Gersh Tolunsky, Feb 18 2023
2024-12-19T11:46:19
oeisdata/seq/A360/A360745.seq
7dcbfc7426a87abf9b201ff119651cf0
A360746
a(n) is the maximum number of locations 1..n-1 which can be reached starting from a(n-1), where jumps from location i to i +- a(i) are permitted (within 1..n-1); a(1)=1. See example.
[ "1", "1", "2", "3", "4", "4", "5", "5", "5", "7", "8", "8", "8", "9", "9", "12", "10", "10", "12", "10", "12", "13", "13", "13", "16", "14", "14", "16", "17", "17", "17", "18", "18", "24", "25", "25", "25", "26", "27", "27", "27", "27", "28", "28", "30", "28", "33", "28", "29", "30", "30", "30", "33", "31", "31", "31", "32", "32", "33", "33", "31", "31", "32", "33", "33", "35", "33", "37" ]
[ "nonn" ]
19
1
3
[ "A358838", "A359005", "A359008", "A360593", "A360594", "A360595", "A360744", "A360745", "A360746" ]
null
Neal Gersh Tolunsky, Feb 18 2023
2023-03-05T11:37:36
oeisdata/seq/A360/A360746.seq
a4ef37d4ec2e448b2d025a03d008866a
A360747
Expansion of Sum_{k>=0} (x * (1 + (k * x)^3))^k.
[ "1", "1", "1", "1", "2", "17", "82", "257", "690", "3484", "26978", "160347", "726085", "3529206", "26885924", "220706533", "1474182023", "8834370165", "65392181686", "604821608674", "5230627589958", "39543579302104", "312733691925723", "3013530105191283", "30474809255061289" ]
[ "nonn" ]
22
0
5
[ "A360479", "A360592", "A360707", "A360747" ]
null
Seiichi Manyama, Feb 19 2023
2023-02-20T03:08:59
oeisdata/seq/A360/A360747.seq
4300571fa3f9567da359590c3b627f09
A360748
Expansion of Sum_{k>=0} (x * (1 + k*x^2))^k.
[ "1", "1", "1", "2", "5", "10", "21", "53", "133", "327", "861", "2361", "6469", "18168", "52757", "155221", "463077", "1412656", "4379917", "13747504", "43834213", "141866555", "464650309", "1541008295", "5176660997", "17586913779", "60400627453", "209746820056", "735953607173", "2607716976945", "9330605338485" ]
[ "nonn" ]
18
0
4
[ "A000930", "A360479", "A360592", "A360730", "A360748", "A360749" ]
null
Seiichi Manyama, Feb 19 2023
2023-02-20T07:12:22
oeisdata/seq/A360/A360748.seq
7c6acd7fa93a5ae686507394b6db80df
A360749
Expansion of Sum_{k>=0} (x * (1 + k*x^3))^k.
[ "1", "1", "1", "1", "2", "5", "10", "17", "30", "64", "146", "315", "649", "1386", "3164", "7381", "16931", "38649", "90406", "217474", "527586", "1277452", "3112371", "7705059", "19336789", "48800634", "123617380", "315671212", "814711955", "2119996540", "5545342621", "14584694613", "38641783669", "103158314515" ]
[ "nonn" ]
13
0
5
[ "A003269", "A360592", "A360731", "A360747", "A360748", "A360749" ]
null
Seiichi Manyama, Feb 19 2023
2023-02-19T09:21:05
oeisdata/seq/A360/A360749.seq
7db827a0fe0df1909a9efa8db0a89df8
A360750
Decimal expansion of the elementary charge over h-bar according to the 2019 SI system in units A/J.
[ "1", "5", "1", "9", "2", "6", "7", "4", "4", "7", "8", "7", "8", "6", "2", "6", "2", "0", "1", "2", "5", "0", "2", "3", "4", "9", "7", "0", "8", "9", "4", "5", "1", "3", "0", "3", "5", "6", "6", "3", "0", "2", "0", "4", "5", "8", "8", "5", "1", "8", "0", "0", "3", "3", "8", "2", "8", "7", "5", "2", "7", "2", "8", "3", "4", "9", "5", "5", "5", "4", "1", "7", "3", "0", "0", "0", "6", "0", "2", "7", "0", "9", "9", "0", "1", "0", "9" ]
[ "nonn", "cons", "easy" ]
13
16
2
[ "A003676", "A081823", "A254181", "A360750" ]
null
Marco Ripà, Feb 19 2023
2023-06-20T10:08:28
oeisdata/seq/A360/A360750.seq
88ac6eca7c6dd8f5f5daaf776d48b43b
A360751
a(n) is the least perfect square average of two consecutive primes with 2*n gap between them, or -1 if no such number exists.
[ "4", "9", "64", "-1", "144", "625", "324", "2601", "-1", "154449", "260100", "1681", "898704", "27225", "114244", "-1", "278784", "223729", "4410000", "25281", "12888100", "4730625", "1512900", "4774225", "-1", "8208225", "6130576", "1121481", "12744900", "34586161", "2433600", "45360225", "9784384", "1271279025", "64064016", "-1", "69956496" ]
[ "sign" ]
13
1
1
[ "A000040", "A000290", "A024675", "A360751" ]
null
Tamas Sandor Nagy, Feb 19 2023
2023-02-20T12:27:37
oeisdata/seq/A360/A360751.seq
fdcbc065502a7b03d4b926f769085b65
A360752
Expansion of Sum_{k>0} (x * (1 + (2 * x)^k))^k.
[ "1", "3", "1", "9", "1", "41", "1", "65", "193", "161", "1", "2433", "1", "897", "10241", "18433", "1", "66049", "1", "403457", "344065", "22529", "1", "7127041", "5242881", "106497", "9437185", "73629697", "1", "332890113", "1", "940572673", "230686721", "2228225", "9395240961", "18828754945", "1", "9961473", "5234491393", "429517701121", "1" ]
[ "nonn" ]
13
1
2
[ "A360733", "A360752" ]
null
Seiichi Manyama, Feb 19 2023
2023-08-02T02:00:27
oeisdata/seq/A360/A360752.seq
15e69e4f4620f4bf9d689fc3627fdfa1
A360753
Matrix inverse of A360657.
[ "1", "0", "1", "0", "-2", "1", "0", "1", "-5", "1", "0", "1", "8", "-9", "1", "0", "2", "4", "29", "-14", "1", "0", "6", "4", "-10", "75", "-20", "1", "0", "24", "4", "-41", "-115", "160", "-27", "1", "0", "120", "-8", "-147", "-196", "-490", "301", "-35", "1", "0", "720", "-136", "-624", "-392", "-231", "-1484", "518", "-44", "1" ]
[ "sign", "easy", "tabl" ]
23
0
5
[ "A132013", "A215534", "A354794", "A354795", "A360657", "A360753" ]
null
Werner Schulte, Feb 21 2023
2023-02-24T01:56:42
oeisdata/seq/A360/A360753.seq
f2a2e76a27d1cfd87f9e969f859733e5
A360754
Expansion of Sum_{k>0} (k * x * (1 + (2 * x)^k))^k.
[ "1", "6", "27", "288", "3125", "47368", "823543", "16793600", "387425673", "10000500000", "285311670611", "8916118771200", "302875106592253", "11112007563452544", "437893890412859375", "18446744108073484288", "827240261886336764177", "39346408077084637733376" ]
[ "nonn" ]
13
1
2
[ "A360732", "A360754" ]
null
Seiichi Manyama, Feb 19 2023
2023-08-02T02:00:31
oeisdata/seq/A360/A360754.seq
e0454dd3a4f5645f82773c2ee660fda8
A360755
Expansion of (1/2) * Sum_{k>0} (2 * x * (1 + x^k))^k.
[ "1", "3", "4", "12", "16", "46", "64", "160", "268", "592", "1024", "2292", "4096", "8640", "16544", "33824", "65536", "133856", "262144", "529576", "1049920", "2108416", "4194304", "8417408", "16777296", "33607680", "67118080", "134334656", "268435456", "537140208", "1073741824", "2148015104", "4295023616", "8591048704" ]
[ "nonn" ]
15
1
2
[ "A360726", "A360755", "A360756" ]
null
Seiichi Manyama, Feb 19 2023
2023-08-02T02:00:34
oeisdata/seq/A360/A360755.seq
5d9394c2037757782e03459a694d3ef5
A360756
Expansion of Sum_{k>0} (x * (1 + 2 * x^k))^k.
[ "1", "3", "1", "5", "1", "11", "1", "9", "13", "11", "1", "45", "1", "15", "41", "49", "1", "79", "1", "117", "85", "23", "1", "297", "81", "27", "145", "309", "1", "483", "1", "481", "221", "35", "561", "1165", "1", "39", "313", "2121", "1", "1143", "1", "1365", "2437", "47", "1", "4081", "449", "3411", "545", "2341", "1", "4699", "5281", "4889", "685", "59", "1", "20445", "1", "63", "6217" ]
[ "nonn" ]
14
1
2
[ "A327249", "A360755", "A360756" ]
null
Seiichi Manyama, Feb 19 2023
2023-08-02T02:00:37
oeisdata/seq/A360/A360756.seq
ef08e7fcc324789e32133be47fdf4ac9
A360757
Numbers k for which the arithmetic derivative of k is a Sophie Germain prime (A005384).
[ "6", "42", "154", "182", "222", "231", "286", "357", "434", "442", "455", "483", "582", "595", "645", "690", "742", "762", "770", "806", "861", "906", "969", "987", "994", "1045", "1066", "1086", "1122", "1162", "1463", "1534", "1547", "1554", "1582", "1738", "1742", "1771", "1798", "1869", "1905", "2065", "2121", "2193", "2265", "2274", "2282", "2365" ]
[ "nonn" ]
22
1
1
[ "A003415", "A005384", "A157037", "A360757" ]
null
Marius A. Burtea, Mar 01 2023
2023-05-23T08:16:14
oeisdata/seq/A360/A360757.seq
3c77a797ecded22a5a0a477f4e16020a
A360758
Numbers k for which k' - 1 and k' + 1 are twin primes, where the prime denotes the arithmetic derivative.
[ "4", "8", "9", "35", "36", "64", "65", "68", "77", "81", "112", "160", "161", "185", "188", "208", "209", "221", "225", "236", "335", "341", "371", "377", "428", "437", "441", "485", "515", "576", "596", "611", "671", "707", "731", "736", "756", "767", "779", "783", "792", "851", "868", "899", "917", "952", "965", "972", "1007", "1028", "1067", "1115", "1152", "1157" ]
[ "nonn" ]
15
1
1
[ "A003415", "A014574", "A022005", "A046138", "A077800", "A212492", "A360758" ]
null
Marius A. Burtea, Mar 01 2023
2023-04-01T23:53:21
oeisdata/seq/A360/A360758.seq
89602a28e2f5be72e999d95abf07fff0
A360759
a(n) = Sum_{d|n} d^(d+n/d) * binomial(d,n/d).
[ "1", "16", "243", "4112", "78125", "1680345", "40353607", "1073766400", "31381060338", "1000000781250", "34522712143931", "1283918489808640", "51185893014090757", "2177953338656796883", "98526125335697265625", "4722366482899710050304", "239072435685151324847153" ]
[ "nonn" ]
21
1
2
[ "A318636", "A327238", "A338685", "A338693", "A338694", "A360712", "A360759" ]
null
Seiichi Manyama, Feb 19 2023
2023-08-02T02:00:40
oeisdata/seq/A360/A360759.seq
c77888c4bf21ad4b99c8930272ea8c97
A360760
a(n) = n^16 + n^15 + n^2 + 1.
[ "1", "4", "98309", "57395638", "5368709137", "183105468776", "3291294892069", "37980492079594", "316659348799553", "2058911320946572", "11000000000000101", "50126978032987934", "200291280469622929", "716602502197270768", "2333521433367183557", "7006302246093750226", "19599665578316398849" ]
[ "nonn", "easy" ]
33
0
2
[ "A010933", "A360760" ]
null
Darío Clavijo, Feb 19 2023
2024-02-20T08:08:36
oeisdata/seq/A360/A360760.seq
d078c28a73e7b4f87b99bcd3c02857e9
A360761
Primes p that divide both 3^k-2 and 5^k-1 for some k.
[ "31", "601", "2593", "20478961", "204700049", "668731841" ]
[ "nonn", "more" ]
23
1
1
[ "A070677", "A360761" ]
null
Robert Israel, Feb 19 2023
2023-02-24T19:32:27
oeisdata/seq/A360/A360761.seq
059b06bdf9fe63a0c8650d30daa22dd9
A360762
a(n) is the least n-gonal number that is the sum of two or more consecutive nonzero n-gonal numbers in more than one way, or -1 if no such number exists.
[ "9", "12880", "20449", "10764222", "794629045", "33205080888", "5985", "13925100" ]
[ "nonn", "more" ]
22
2
1
[ "A057145", "A062681", "A307608", "A307614", "A343777", "A360762", "A360777" ]
null
Ilya Gutkovskiy, Feb 19 2023
2025-02-16T08:34:04
oeisdata/seq/A360/A360762.seq
e77cef486503438d73e11ec64a02d998
A360763
Number T(n,k) of multisets of nonempty strict integer partitions with a total of k parts and total sum of n; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
[ "1", "0", "1", "0", "1", "1", "0", "1", "2", "1", "0", "1", "3", "2", "1", "0", "1", "4", "4", "2", "1", "0", "1", "5", "8", "5", "2", "1", "0", "1", "6", "11", "10", "5", "2", "1", "0", "1", "7", "16", "18", "11", "5", "2", "1", "0", "1", "8", "22", "28", "22", "12", "5", "2", "1", "0", "1", "9", "28", "45", "39", "24", "12", "5", "2", "1", "0", "1", "10", "35", "63", "67", "46", "25", "12", "5", "2", "1", "0", "1", "11", "44", "89", "106", "86", "50", "26", "12", "5", "2", "1" ]
[ "nonn", "tabl" ]
33
0
9
[ "A000007", "A000009", "A001477", "A008289", "A055884", "A057427", "A089259", "A285229", "A360742", "A360763", "A360764", "A360784", "A360785" ]
null
Alois P. Heinz, Feb 19 2023
2023-09-12T12:02:46
oeisdata/seq/A360/A360763.seq
3cc020f6c537f5925aa86481d6f12205
A360764
Number T(n,k) of sets of nonempty strict integer partitions with a total of k parts and total sum of n; triangle T(n,k), n>=0, 0<=k<=max(i:T(n,i)>0), read by rows.
[ "1", "0", "1", "0", "1", "0", "1", "2", "0", "1", "2", "1", "0", "1", "4", "2", "0", "1", "4", "6", "1", "0", "1", "6", "8", "4", "0", "1", "6", "13", "9", "1", "0", "1", "8", "18", "16", "6", "0", "1", "8", "24", "29", "13", "2", "0", "1", "10", "30", "43", "29", "6", "0", "1", "10", "39", "64", "52", "19", "1", "0", "1", "12", "46", "89", "89", "42", "7", "0", "1", "12", "56", "122", "139", "85", "22", "1" ]
[ "nonn", "tabf" ]
30
0
8
[ "A000007", "A000009", "A008289", "A050342", "A052928", "A055884", "A057427", "A330462", "A360742", "A360763", "A360764" ]
null
Alois P. Heinz, Feb 19 2023
2023-11-17T11:57:00
oeisdata/seq/A360/A360764.seq
74157e3f67f3030ad01ab9f6f4392467
A360765
Numbers k that are neither prime powers nor squarefree, such that A007947(k) * A053669(k) < k.
[ "36", "40", "45", "48", "50", "54", "56", "63", "72", "75", "80", "88", "96", "98", "99", "100", "104", "108", "112", "117", "135", "136", "144", "147", "152", "153", "160", "162", "171", "175", "176", "184", "189", "192", "196", "200", "207", "208", "216", "224", "225", "232", "240", "242", "245", "248", "250", "252", "261", "270", "272", "275", "279", "280", "288", "294", "296", "297", "300", "304", "315", "320", "324", "325" ]
[ "nonn" ]
9
1
1
[ "A001221", "A001222", "A007947", "A053669", "A126706", "A246547", "A360765" ]
null
Michael De Vlieger, Mar 05 2023
2023-03-07T02:32:48
oeisdata/seq/A360/A360765.seq
33854ca65e725d6e8e39081817d473b8
A360766
a(0) = 0; a(n) = ( (n + sqrt(n))^n - (n - sqrt(n))^n )/(2 * sqrt(n)).
[ "0", "1", "4", "30", "320", "4400", "73872", "1462552", "33325056", "858283776", "24641000000", "779935205984", "26972930949120", "1011642325897216", "40890444454377728", "1771640957790000000", "81896889467638120448", "4022826671022707900416", "209224123984489179202560" ]
[ "nonn", "easy" ]
47
0
3
[ "A007070", "A030192", "A084062", "A093145", "A154237", "A360766", "A361290" ]
null
Seiichi Manyama, Mar 11 2023
2023-03-16T04:54:19
oeisdata/seq/A360/A360766.seq
cd179456414e97bbf6e3f38f3ec54e1f
A360767
Numbers k that are neither prime power nor squarefree, such that k/rad(k) < q, where rad(k) = A007947(k) and prime q = A119288(k).
[ "12", "20", "28", "40", "44", "45", "52", "56", "60", "63", "68", "76", "84", "88", "92", "99", "104", "116", "117", "124", "132", "136", "140", "148", "152", "153", "156", "164", "171", "172", "175", "176", "184", "188", "204", "207", "208", "212", "220", "228", "232", "236", "244", "248", "260", "261", "268", "272", "275", "276", "279", "280", "284", "292", "296", "297", "304", "308", "315", "316", "325", "328", "332", "333" ]
[ "nonn", "easy" ]
14
1
1
[ "A007947", "A013929", "A024619", "A119288", "A126706", "A355432", "A360767", "A360768" ]
null
Michael De Vlieger, Feb 28 2023
2023-03-04T02:08:55
oeisdata/seq/A360/A360767.seq
ba243048d2e300817bb1bcf20edd061d
A360768
Numbers k that are neither prime powers nor squarefree, such that k/rad(k) >= q, where rad(k) = A007947(k) and prime q = A119288(k).
[ "18", "24", "36", "48", "50", "54", "72", "75", "80", "90", "96", "98", "100", "108", "112", "120", "126", "135", "144", "147", "150", "160", "162", "168", "180", "189", "192", "196", "198", "200", "216", "224", "225", "234", "240", "242", "245", "250", "252", "264", "270", "288", "294", "300", "306", "312", "320", "324", "336", "338", "342", "350", "352", "360", "363", "375", "378", "384", "392", "396", "400", "405", "408" ]
[ "nonn" ]
16
1
1
[ "A007947", "A013929", "A024619", "A119288", "A126706", "A355432", "A360768" ]
null
Michael De Vlieger, Feb 22 2023
2023-03-04T02:08:45
oeisdata/seq/A360/A360768.seq
acfdb1d73004107a2284ae490a590e86
A360769
Odd numbers that are neither prime powers nor squarefree.
[ "45", "63", "75", "99", "117", "135", "147", "153", "171", "175", "189", "207", "225", "245", "261", "275", "279", "297", "315", "325", "333", "351", "363", "369", "375", "387", "405", "423", "425", "441", "459", "475", "477", "495", "507", "513", "525", "531", "539", "549", "567", "575", "585", "603", "605", "621", "637", "639", "657", "675", "693", "711", "725", "735", "747", "765", "775", "783", "801", "819", "825" ]
[ "nonn" ]
21
1
1
[ "A001221", "A001222", "A005418", "A013929", "A024619", "A126706", "A360769" ]
null
Michael De Vlieger, Feb 28 2023
2023-03-04T02:08:28
oeisdata/seq/A360/A360769.seq
3c1ce448b036c189a9200b0e46c67127
A360770
Expansion of Sum_{k>0} (x * (k + x^k))^k.
[ "1", "5", "27", "260", "3125", "46684", "823543", "16777472", "387420498", "10000003125", "285311670611", "8916100495009", "302875106592253", "11112006826381559", "437893890380860625", "18446744073726328848", "827240261886336764177", "39346408075296925015353" ]
[ "nonn" ]
16
1
2
[ "A260148", "A338693", "A360712", "A360770", "A360771", "A360774", "A360775", "A360776" ]
null
Seiichi Manyama, Feb 20 2023
2023-08-02T01:59:59
oeisdata/seq/A360/A360770.seq
5df51346b17410928a8f83e4b32b8349
A360771
Expansion of Sum_{k>=0} (x * (2 + x^k))^k.
[ "1", "2", "5", "8", "20", "32", "77", "128", "288", "518", "1104", "2048", "4313", "8192", "16832", "32848", "66568", "131072", "264688", "524288", "1053737", "2097824", "4205568", "8388608", "16803744", "33554442", "67162112", "134222336", "268550704", "536870912", "1073999165", "2147483648", "4295493376", "8589962752" ]
[ "nonn" ]
15
0
2
[ "A217668", "A260148", "A360771" ]
null
Seiichi Manyama, Feb 20 2023
2023-08-02T02:00:02
oeisdata/seq/A360/A360771.seq
5af160d5823e5f7692cf07984cc67759
A360772
List of distinct numbers that are powers of odd-indexed Fibonacci numbers or even powers of nonzero even-indexed Fibonacci numbers.
[ "1", "2", "4", "5", "8", "9", "13", "16", "25", "32", "34", "64", "81", "89", "125", "128", "169", "233", "256", "441", "512", "610", "625", "729", "1024", "1156", "1597", "2048", "2197", "3025", "3125", "4096", "4181", "6561", "7921", "8192", "10946", "15625", "16384", "20736", "28561", "28657", "32768", "39304", "54289", "59049", "65536", "75025", "78125" ]
[ "nonn" ]
12
1
2
[ "A000045", "A001519", "A001906", "A103323", "A105317", "A235383", "A254719", "A360772" ]
null
Amiram Eldar, Feb 20 2023
2025-01-05T19:51:42
oeisdata/seq/A360/A360772.seq
7e4c6f64c339c36153bec9292057378d
A360773
Number of ways to tile a 2n X 2n square using rectangles with distinct dimensions such that the sum of the rectangles perimeters equals the area of the square.
[ "0", "1", "8", "1024", "620448" ]
[ "nonn", "more" ]
5
1
3
[ "A004003", "A065072", "A099390", "A182275", "A360256", "A360498", "A360499", "A360725", "A360773" ]
null
Scott R. Shannon and N. J. A. Sloane, Feb 20 2023
2023-02-20T08:21:22
oeisdata/seq/A360/A360773.seq
cdf33d6235c662f8f77861335f7e328c
A360774
Expansion of Sum_{k>=0} (x * (k + x))^k.
[ "1", "1", "5", "31", "284", "3390", "49878", "871465", "17620450", "404554997", "10394845097", "295485704544", "9205957047661", "311922101632409", "11419004058232897", "449146827324857447", "18889836751306735360", "845892838094616177138", "40182354573647684880446" ]
[ "nonn" ]
9
0
3
[ "A360611", "A360618", "A360774", "A360775", "A360776" ]
null
Seiichi Manyama, Feb 20 2023
2023-02-20T07:50:49
oeisdata/seq/A360/A360774.seq
9d233af1777b50b4d9268ee856bbda03
A360775
Expansion of Sum_{k>=0} (x * (k + x^2))^k.
[ "1", "1", "4", "28", "260", "3152", "46913", "826677", "16823968", "388245283", "10016796672", "285699444297", "8926107792609", "303160590533808", "11120927427841820", "438196895219227683", "18457860168281435172", "827678295600605015006", "39364859979651634985089" ]
[ "nonn" ]
10
0
3
[ "A360018", "A360727", "A360774", "A360775", "A360776" ]
null
Seiichi Manyama, Feb 20 2023
2023-02-20T07:50:45
oeisdata/seq/A360/A360775.seq
ab2e572c2c65ac41ebf4f8d875df6227
A360776
Expansion of Sum_{k>=0} (x * (k + x^3))^k.
[ "1", "1", "4", "27", "257", "3129", "46683", "823799", "16780342", "387467154", "10000823639", "285328449077", "8916487888186", "302885106945216", "11112292144568909", "437902806653498835", "18447046953316227905", "827251374022851280231", "39346845973273509115167" ]
[ "nonn" ]
9
0
3
[ "A360032", "A360728", "A360774", "A360775", "A360776" ]
null
Seiichi Manyama, Feb 20 2023
2023-02-20T07:50:28
oeisdata/seq/A360/A360776.seq
8b77c331e81177cc978b5455fe4c4b0a
A360777
a(n) is the index of the least n-gonal number that is the sum of two or more consecutive nonzero n-gonal numbers in more than one way, or -1 if no such number exists.
[ "9", "160", "143", "2679", "19933", "115248", "45", "1995" ]
[ "nonn", "more" ]
13
2
1
[ "A057145", "A360762", "A360777" ]
null
Ilya Gutkovskiy, Feb 20 2023
2025-02-16T08:34:04
oeisdata/seq/A360/A360777.seq
c28baf189e80b8f98aa902b81d505ea3
A360778
Smallest number k such that n + k is a refactorable number.
[ "1", "0", "0", "5", "4", "3", "2", "1", "0", "0", "2", "1", "0", "5", "4", "3", "2", "1", "0", "5", "4", "3", "2", "1", "0", "11", "10", "9", "8", "7", "6", "5", "4", "3", "2", "1", "0", "3", "2", "1", "0", "15", "14", "13", "12", "11", "10", "9", "8", "7", "6", "5", "4", "3", "2", "1", "0", "3", "2", "1", "0", "11", "10", "9", "8", "7", "6", "5", "4", "3", "2", "1", "0", "7", "6", "5", "4", "3", "2", "1", "0", "3", "2", "1", "0", "3", "2", "1", "0" ]
[ "nonn" ]
12
0
4
[ "A033950", "A360778" ]
null
Ctibor O. Zizka, Feb 20 2023
2023-03-05T17:08:35
oeisdata/seq/A360/A360778.seq
5a036fa8f00af1e0065d7fe9aa415c33
A360779
Refactorable numbers gaps: differences between consecutive refactorable numbers.
[ "1", "6", "1", "3", "6", "6", "12", "4", "16", "4", "12", "8", "4", "4", "8", "8", "4", "20", "4", "4", "16", "4", "24", "4", "20", "21", "3", "4", "8", "8", "4", "24", "12", "8", "32", "16", "4", "12", "12", "4", "8", "12", "28", "17", "3", "4", "2", "18", "4", "8", "8", "4", "12", "12", "20", "24", "4", "4", "16", "16", "12", "13", "7", "4", "4", "24", "8", "12", "24", "4", "8", "12", "44", "16", "12", "4", "16", "4", "24" ]
[ "nonn" ]
18
1
2
[ "A033950", "A036896", "A036898", "A114617", "A360779" ]
null
Ctibor O. Zizka, Feb 20 2023
2023-03-05T17:09:05
oeisdata/seq/A360/A360779.seq
79982f144b20723cff8b03e6eeb589c7
A360780
Least refactorable number > n.
[ "1", "2", "8", "8", "8", "8", "8", "8", "9", "12", "12", "12", "18", "18", "18", "18", "18", "18", "24", "24", "24", "24", "24", "24", "36", "36", "36", "36", "36", "36", "36", "36", "36", "36", "36", "36", "40", "40", "40", "40", "56", "56", "56", "56", "56", "56", "56", "56", "56", "56", "56", "56", "56", "56", "56", "56", "60", "60", "60", "60", "72", "72", "72", "72", "72", "72", "72", "72", "72" ]
[ "nonn" ]
10
0
2
[ "A033950", "A360780" ]
null
Ctibor O. Zizka, Feb 20 2023
2023-03-05T17:08:29
oeisdata/seq/A360/A360780.seq
23efa6ea233e3f01a15a4c38ba570ba5
A360781
Primes p such that at least one number remains prime when p is bracketed by a single digit d; that is, at least one instance of d//p//d is prime where // means concatenation.
[ "2", "3", "5", "7", "17", "19", "23", "29", "31", "37", "41", "43", "47", "53", "59", "61", "67", "71", "73", "79", "83", "101", "103", "107", "109", "113", "131", "139", "149", "151", "157", "163", "173", "179", "191", "193", "197", "211", "223", "227", "233", "239", "241", "251", "257", "263", "269", "271", "277", "281", "283", "293", "307", "311", "313", "317", "331" ]
[ "nonn", "base" ]
19
1
1
[ "A000040", "A059694", "A069687", "A069688", "A069689", "A069690", "A360781" ]
null
Harvey P. Dale, Feb 20 2023
2023-02-24T20:21:41
oeisdata/seq/A360/A360781.seq
6defa4b258c21096eabf8ead16eef027
A360782
Expansion of Sum_{k>=0} x^k / (1 - k*x^2)^(k+1).
[ "1", "1", "1", "3", "7", "16", "45", "125", "363", "1127", "3561", "11696", "39727", "138113", "494213", "1811075", "6784115", "25985928", "101520833", "404305549", "1640002039", "6767576175", "28395916893", "121048681024", "523902418555", "2300906314849", "10248029334297", "46266088140291" ]
[ "nonn", "easy" ]
17
0
4
[ "A000045", "A000248", "A360592", "A360782", "A360783" ]
null
Seiichi Manyama, Feb 20 2023
2023-02-21T02:09:24
oeisdata/seq/A360/A360782.seq
961e57b86538d8433772f80e66c0daff
A360783
Expansion of Sum_{k>=0} x^k / (1 - k*x^3)^(k+1).
[ "1", "1", "1", "1", "3", "7", "13", "24", "55", "133", "301", "678", "1639", "4120", "10253", "25591", "65869", "173551", "459493", "1225379", "3325123", "9162046", "25451181", "71296499", "202144225", "579612934", "1675822453", "4885178596", "14376297345", "42690792651", "127757371105", "385241085261", "1170960103855" ]
[ "nonn", "easy" ]
12
0
5
[ "A000248", "A000930", "A360782", "A360783" ]
null
Seiichi Manyama, Feb 20 2023
2023-02-20T12:27:25
oeisdata/seq/A360/A360783.seq
f93881ca331a619451c16e7cdd9e5b1c
A360784
Number of multisets of nonempty strict integer partitions with a total of n parts and total sum of 2n.
[ "1", "1", "3", "8", "18", "39", "86", "175", "352", "688", "1318", "2472", "4576", "8322", "14959", "26560", "46657", "81130", "139866", "239047", "405496", "682891", "1142466", "1899344", "3139432", "5160455", "8438871", "13732292", "22242647", "35867937", "57597730", "92121145", "146775205", "232998683", "368579188", "581091003" ]
[ "nonn" ]
15
0
3
[ "A000009", "A360763", "A360784", "A360785" ]
null
Alois P. Heinz, Feb 20 2023
2023-11-21T08:39:34
oeisdata/seq/A360/A360784.seq
3099346becbd338c51070dbe2135437d
A360785
Number of multisets of nonempty strict integer partitions with a total of 2n parts and total sum of 3n.
[ "1", "2", "5", "12", "26", "54", "112", "220", "427", "812", "1518", "2790", "5074", "9096", "16144", "28360", "49367", "85180", "145867", "247886", "418426", "701702", "1169673", "1938498", "3195497", "5240386", "8552308", "13892638", "22468406", "36184636", "58040397", "92737842", "147631545", "234184172", "370215442", "583343070" ]
[ "nonn" ]
20
0
2
[ "A360763", "A360784", "A360785" ]
null
Alois P. Heinz, Feb 20 2023
2023-12-09T09:00:12
oeisdata/seq/A360/A360785.seq
c10b266f4a4f693a55544d1887816ec9
A360786
Number of ways to place two dimers on an n-cube.
[ "0", "2", "42", "400", "2840", "17376", "97440", "516608", "2634624", "13058560", "63320576", "301707264", "1417009152", "6575120384", "30195425280", "137430827008", "620604391424", "2783097520128", "12403773407232", "54975376916480", "242441862512640", "1064326263734272", "4653131038195712", "20266193591992320" ]
[ "nonn", "easy" ]
25
1
2
[ "A001787", "A045310", "A192437", "A302235", "A360786" ]
null
Krishnan Balasubramanian, Feb 20 2023
2025-02-16T08:34:04
oeisdata/seq/A360/A360786.seq
ab53ba7703edc786eb58efa5260afa37
A360787
Expansion of Sum_{k>=0} x^k / (1 - (k*x)^2)^(k+1).
[ "1", "1", "1", "3", "13", "40", "177", "965", "4733", "28103", "184065", "1191888", "8713549", "67005689", "528870257", "4526024267", "40051790333", "368513578472", "3583302492545", "35868588067501", "373781214260749", "4052932682659599", "45218033687522481", "523234757502985824", "6245693941097387773" ]
[ "nonn", "easy" ]
13
0
4
[ "A000248", "A360592", "A360782", "A360787", "A360788" ]
null
Seiichi Manyama, Feb 20 2023
2023-02-21T02:09:20
oeisdata/seq/A360/A360787.seq
a3e13e544657b0e585c314dab4b805c5
A360788
Expansion of Sum_{k>=0} x^k / (1 - (k*x)^3)^(k+1).
[ "1", "1", "1", "1", "3", "25", "109", "324", "1135", "8803", "64189", "337854", "1707319", "13421410", "121248893", "894378619", "6082868725", "53046554917", "543432115477", "4989423130739", "42565774604131", "421544374075072", "4781440892689533", "51342685464272591", "522295380717090265" ]
[ "nonn", "easy" ]
9
0
5
[ "A000248", "A360783", "A360787", "A360788" ]
null
Seiichi Manyama, Feb 20 2023
2023-02-20T12:27:33
oeisdata/seq/A360/A360788.seq
b49811fadf0502b6f97bf83199c79f2f
A360789
Least prime p such that p mod primepi(p) = n.
[ "2", "3", "5", "7", "379", "23", "401", "61", "59", "29", "67", "71", "467", "79", "83", "179", "431", "89", "176557", "191", "24419", "491", "97", "101", "499", "1213", "3169", "3191", "523", "229", "3187", "223", "3203", "8609", "3163", "251", "176509", "257", "24509", "263", "3253", "269", "547", "3347", "1304867", "293" ]
[ "nonn" ]
27
0
1
[ "A004648", "A038625", "A048891", "A052013", "A073325", "A073436", "A162567", "A171430", "A171431", "A171432", "A171434", "A360789" ]
null
Robert G. Wilson v, Feb 20 2023
2023-03-19T03:40:54
oeisdata/seq/A360/A360789.seq
10be7b30ef53b2f6139703835ce6565a
A360790
Squared length of diagonal of right trapezoid with three consecutive prime length sides.
[ "8", "13", "41", "53", "137", "173", "305", "397", "533", "877", "977", "1373", "1697", "1885", "2245", "2813", "3517", "3737", "4493", "5077", "5345", "6277", "6953", "7937", "9413", "10217", "10613", "11465", "12077", "12785", "16165", "17165", "18869", "19325", "22237", "22837", "24665", "26605", "27925", "29933", "32141", "32765", "36497", "37253", "38953", "39745" ]
[ "nonn" ]
76
1
1
[ "A001248", "A076821", "A106171", "A131019", "A360790" ]
null
Aaron T Cowan, Feb 20 2023
2023-03-11T06:22:13
oeisdata/seq/A360/A360790.seq
764ede29a28614c7f27df72dfc3a4aa5
A360791
Sum of all prime encoded complete partitions of n.
[ "1", "2", "4", "14", "28", "94", "218", "588", "1366", "3618", "8134", "20320", "45592", "105810", "236960", "539392", "1174530", "2612436", "5628606", "12226350", "26130568", "55938126", "117997774", "249680514", "523032956", "1094500962", "2275886514", "4727461792", "9762182762", "20148991512", "41403646304", "84961079990" ]
[ "nonn" ]
18
0
2
[ "A126796", "A215366", "A258118", "A360713", "A360791" ]
null
Alois P. Heinz, Feb 21 2023
2023-02-21T16:05:06
oeisdata/seq/A360/A360791.seq
e02e38373dab4843932e1308b88fb199
A360792
Integer portion of area of inscribed circle in a regular polygon having n sides of unit length.
[ "0", "0", "1", "2", "3", "4", "5", "7", "9", "10", "12", "15", "17", "19", "22", "25", "28", "31", "34", "37", "41", "45", "49", "53", "57", "61", "66", "71", "75", "80", "86", "91", "96", "102", "108", "114", "120", "126", "133", "139", "146", "153", "160", "167", "175", "182", "190", "198", "206", "214", "223", "231", "240", "249", "258", "267", "276", "285", "295", "305" ]
[ "nonn" ]
18
3
4
[ "A062299", "A062300", "A360792" ]
null
A. Timothy Royappa, Feb 20 2023
2025-04-04T22:36:21
oeisdata/seq/A360/A360792.seq
70e6edb1c2e9766290c4171fd474581e
A360793
Numbers of the form m*p^3, where m > 1 is squarefree and prime p does not divide m.
[ "24", "40", "54", "56", "88", "104", "120", "135", "136", "152", "168", "184", "189", "232", "248", "250", "264", "270", "280", "296", "297", "312", "328", "344", "351", "375", "376", "378", "408", "424", "440", "456", "459", "472", "488", "513", "520", "536", "552", "568", "584", "594", "616", "621", "632", "664", "680", "686", "696", "702", "712", "728", "744", "750" ]
[ "nonn" ]
40
1
1
[ "A000005", "A001221", "A001222", "A013661", "A030078", "A036537", "A048109", "A072357", "A126706", "A190641", "A360793" ]
null
David James Sycamore, Feb 21 2023
2025-02-26T01:55:24
oeisdata/seq/A360/A360793.seq
74531b118c99797f1294366d05264493
A360794
Expansion of Sum_{k>0} x^k / (1 - k * x^k)^(k+1).
[ "1", "3", "4", "11", "6", "43", "8", "109", "100", "281", "12", "1507", "14", "1863", "3376", "6937", "18", "26245", "20", "53211", "63022", "67739", "24", "572413", "78776", "372945", "1087048", "1761719", "30", "7362871", "32", "9947953", "16897486", "10027349", "8011116", "123101515", "38", "49807779", "241823440", "361722421", "42" ]
[ "nonn" ]
15
1
2
[ "A081543", "A324158", "A360782", "A360783", "A360794" ]
null
Seiichi Manyama, Feb 21 2023
2023-07-31T02:25:05
oeisdata/seq/A360/A360794.seq
79e9226fe656d9f921dc4215112b0b00
A360795
Expansion of Sum_{k>0} x^k / (1 - (k * x)^k)^(k+1).
[ "1", "3", "4", "17", "6", "211", "8", "1929", "7300", "22601", "12", "1724809", "14", "6703047", "223678576", "738787345", "18", "65630598229", "20", "2119646503661", "24448573943662", "3423809253371", "24", "21453113652593665", "12016296386718776", "4240253019018225", "8255251542208471048", "67251293544533119589", "30" ]
[ "nonn" ]
15
1
2
[ "A339481", "A360787", "A360788", "A360794", "A360795" ]
null
Seiichi Manyama, Feb 21 2023
2023-08-02T02:00:05
oeisdata/seq/A360/A360795.seq
aa15fd4752c879bf918bb5670b8e96f3
A360796
a(n) > n is the smallest integer such that there exist integers n < c <= d < a(n) satisfying n^2 + a(n)^2 = c^2 + d^2.
[ "7", "9", "11", "13", "14", "17", "17", "19", "20", "25", "23", "29", "26", "27", "29", "37", "31", "40", "34", "35", "38", "46", "39", "41", "44", "43", "44", "54", "47", "58", "49", "51", "56", "53", "54", "67", "62", "59", "59", "70", "62", "73", "64", "65", "74", "78", "69", "71", "71", "75", "74", "86", "76", "77", "79", "83", "92", "93", "83", "103" ]
[ "nonn" ]
31
1
1
[ "A000404", "A007692", "A360619", "A360796" ]
null
Giedrius Alkauskas, Feb 21 2023
2023-08-05T22:01:14
oeisdata/seq/A360/A360796.seq
43cd946e7be72026a0d7a9b16b6a5ac1
A360797
Expansion of Sum_{k>0} x^k / (1 - 2 * x^k)^(k+1).
[ "1", "5", "13", "39", "81", "225", "449", "1115", "2345", "5373", "11265", "25483", "53249", "116497", "246405", "529195", "1114113", "2372741", "4980737", "10515511", "22025617", "46204953", "96468993", "201506607", "419432417", "872787997", "1811981789", "3758970975", "7784628225", "16108217801", "33285996545", "68723976779" ]
[ "nonn" ]
15
1
2
[ "A360797", "A360798" ]
null
Seiichi Manyama, Feb 21 2023
2023-07-31T02:25:08
oeisdata/seq/A360/A360797.seq
c842b3411bbeaf169694dc38935a1b56
A360798
Expansion of Sum_{k>0} x^k / (1 - (2 * x)^k)^(k+1).
[ "1", "5", "13", "45", "81", "321", "449", "1745", "2945", "9153", "11265", "60609", "53249", "230401", "410625", "1259777", "1114113", "7263233", "4980737", "31337473", "44630017", "115367937", "96468993", "937283585", "551550977", "2399256577", "4594597889", "14579646465", "7784628225", "89894944769", "33285996545" ]
[ "nonn" ]
14
1
2
[ "A360797", "A360798" ]
null
Seiichi Manyama, Feb 21 2023
2023-08-02T02:00:08
oeisdata/seq/A360/A360798.seq
e92679924a231b329741a4c368793d7f
A360799
Numbers m with m mod 3 = q, q != 2, such that the number of ones in its base-2 representation is even if q=0 and odd if q=1.
[ "0", "1", "3", "4", "6", "7", "9", "12", "13", "15", "16", "18", "19", "22", "24", "25", "27", "28", "30", "31", "33", "36", "37", "39", "45", "48", "49", "51", "52", "54", "55", "57", "60", "61", "63", "64", "66", "67", "70", "72", "73", "75", "76", "78", "79", "82", "88", "90", "91", "94", "96", "97", "99", "100", "102", "103", "105", "108", "109", "111", "112", "114", "115", "118", "120", "121" ]
[ "nonn" ]
16
0
3
[ "A001835", "A003775", "A028469", "A028471", "A180963", "A187616", "A360799", "A360800" ]
null
Gerhard Kirchner, Feb 24 2023
2023-03-31T14:58:11
oeisdata/seq/A360/A360799.seq
78a7b4a7b0d7c7e29227572770b7f290
A360800
Numbers Sum_{i=1..2r+1} 2^k(i) such that k(1) is even and, for r > 0 and i < 2r+1, the difference k(i+1)-k(i) is > 0 and odd.
[ "1", "4", "7", "16", "19", "25", "28", "31", "64", "67", "73", "76", "79", "97", "100", "103", "112", "115", "121", "124", "127", "256", "259", "265", "268", "271", "289", "292", "295", "304", "307", "313", "316", "319", "385", "388", "391", "400", "403", "409", "412", "415", "448", "451", "457", "460", "463", "481", "484", "487", "496", "499", "505", "508", "511", "1024" ]
[ "nonn" ]
9
1
2
[ "A001835", "A003775", "A028469", "A028471", "A180963", "A187616", "A360799", "A360800" ]
null
Gerhard Kirchner, Feb 24 2023
2023-03-31T15:00:14
oeisdata/seq/A360/A360800.seq
7e9ae8b1438fe717f628ec529ef6bc39