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-14,827
666,262,453B
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1999-12-11 03:00:00
2025-07-19 00:40:46
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A377804
Decimal expansion of the surface area of a snub dodecahedron with unit edge length.
[ "5", "5", "2", "8", "6", "7", "4", "4", "9", "5", "8", "4", "4", "5", "1", "4", "8", "9", "4", "3", "6", "5", "7", "0", "7", "0", "5", "5", "8", "7", "8", "0", "7", "6", "2", "5", "3", "1", "7", "4", "4", "5", "9", "5", "1", "1", "6", "3", "2", "9", "9", "9", "2", "5", "1", "1", "6", "0", "1", "2", "7", "6", "0", "7", "3", "3", "2", "5", "0", "8", "8", "2", "4", "4", "6", "8", "3", "5", "9", "5", "5", "1", "7", "6", "1", "2", "2", "1", "8", "6" ]
[ "nonn", "cons", "easy" ]
12
2
1
[ "A002194", "A131595", "A377804", "A377805", "A377806", "A377807" ]
null
Paolo Xausa, Nov 08 2024
2025-02-11T14:39:07
oeisdata/seq/A377/A377804.seq
40f51dc6d40c37dea2be2ca9bd0233aa
A377805
Decimal expansion of the volume of a snub dodecahedron with unit edge length.
[ "3", "7", "6", "1", "6", "6", "4", "9", "9", "6", "2", "7", "3", "3", "3", "6", "2", "9", "7", "5", "7", "7", "7", "6", "7", "3", "6", "7", "1", "3", "0", "2", "7", "1", "4", "3", "4", "0", "3", "5", "5", "2", "8", "9", "8", "7", "3", "4", "8", "8", "0", "9", "8", "9", "6", "0", "4", "9", "6", "8", "9", "7", "3", "0", "2", "9", "9", "3", "6", "2", "0", "0", "7", "5", "7", "8", "7", "6", "4", "1", "6", "7", "9", "4", "6", "0", "9", "2", "9", "4" ]
[ "nonn", "cons", "easy" ]
21
2
1
[ "A001622", "A090550", "A102769", "A104457", "A134946", "A377804", "A377805", "A377806", "A377807", "A377849" ]
null
Paolo Xausa, Nov 09 2024
2025-03-10T12:30:01
oeisdata/seq/A377/A377805.seq
1ab0747056ffe687f20296733392df9e
A377806
Decimal expansion of the circumradius of a snub dodecahedron with unit edge length.
[ "2", "1", "5", "5", "8", "3", "7", "3", "7", "5", "1", "1", "5", "6", "3", "9", "7", "0", "1", "8", "3", "6", "6", "2", "9", "0", "7", "6", "6", "9", "3", "0", "5", "8", "2", "7", "7", "0", "1", "6", "8", "5", "1", "2", "1", "8", "7", "7", "4", "8", "1", "1", "8", "2", "2", "4", "1", "2", "2", "1", "5", "4", "3", "0", "1", "2", "0", "0", "6", "7", "0", "8", "0", "9", "4", "9", "4", "8", "4", "0", "0", "0", "5", "3", "4", "2", "9", "9", "2", "6" ]
[ "nonn", "cons", "easy" ]
11
1
1
[ "A179296", "A377804", "A377805", "A377806", "A377807", "A377849" ]
null
Paolo Xausa, Nov 10 2024
2025-02-11T14:39:21
oeisdata/seq/A377/A377806.seq
d379fdcd0c89e2cd4e7c5132d98dcb02
A377807
Decimal expansion of the midradius of a snub dodecahedron with unit edge length.
[ "2", "0", "9", "7", "0", "5", "3", "8", "3", "5", "2", "5", "2", "0", "8", "7", "9", "9", "2", "4", "0", "3", "9", "5", "9", "0", "5", "2", "3", "4", "8", "2", "8", "6", "2", "4", "0", "0", "3", "0", "8", "3", "9", "7", "3", "0", "5", "8", "1", "0", "3", "0", "7", "6", "2", "7", "3", "1", "7", "0", "6", "1", "7", "3", "1", "2", "7", "0", "5", "2", "9", "1", "4", "2", "5", "7", "7", "7", "5", "4", "5", "5", "3", "7", "3", "4", "0", "9", "4", "8" ]
[ "nonn", "cons", "easy" ]
9
1
1
[ "A239798", "A377804", "A377805", "A377806", "A377807", "A377849" ]
null
Paolo Xausa, Nov 10 2024
2025-02-11T09:56:14
oeisdata/seq/A377/A377807.seq
698414d5cd5854c4a4fbd2f631a1b546
A377808
Prime numbers p such that the set of integers E = {1,2,3,...,p} can be divided into two subsets of consecutive integers E1 = {1,2,...,N} and E2 = {N+1,N+2,...,p} such that phi(1+2+...+N) = phi(N+1,N+2+...+p) for some N.
[ "2", "3", "5", "13", "47", "67", "73", "83", "89", "103", "107", "137", "163", "179", "211", "239", "317", "331", "337", "347", "349", "359", "373", "401", "433", "491", "557", "599", "641", "659", "661", "683", "701", "743", "769", "787", "811", "827", "857", "983", "1069", "1093", "1109", "1117", "1123", "1181", "1217", "1259", "1279", "1289", "1303", "1361", "1429" ]
[ "nonn" ]
15
1
1
[ "A000010", "A377808" ]
null
Michel Lagneau, Nov 08 2024
2024-12-08T17:15:42
oeisdata/seq/A377/A377808.seq
0d21f0f77f8ae20d46964e1960b21808
A377809
k*(k+3)/2 appears k times.
[ "2", "5", "5", "9", "9", "9", "14", "14", "14", "14", "20", "20", "20", "20", "20", "27", "27", "27", "27", "27", "27", "35", "35", "35", "35", "35", "35", "35", "44", "44", "44", "44", "44", "44", "44", "44", "54", "54", "54", "54", "54", "54", "54", "54", "54", "65", "65", "65", "65", "65", "65", "65", "65", "65", "65", "77", "77", "77", "77", "77", "77", "77", "77", "77", "77", "77", "90" ]
[ "nonn", "easy", "tabl" ]
20
1
1
[ "A000096", "A002024", "A119713", "A377809" ]
null
Chai Wah Wu, Nov 08 2024
2024-11-09T17:28:12
oeisdata/seq/A377/A377809.seq
2d395c9a0be491be7699b8a070b21c88
A377810
E.g.f. satisfies A(x) = exp(x * A(x)) / (1 - x)^2.
[ "1", "3", "17", "154", "1993", "34066", "728209", "18733926", "564117425", "19473863986", "758421401401", "32901791851006", "1573602042306265", "82267318018246986", "4667656830688700801", "285662368622361581206", "18758565855176593500385", "1315663025587514658845026", "98160436697525045768511721" ]
[ "nonn" ]
9
0
2
[ "A352410", "A362775", "A377742", "A377810", "A377811" ]
null
Seiichi Manyama, Nov 08 2024
2025-02-16T08:34:07
oeisdata/seq/A377/A377810.seq
feff318321a6848dbd52a7c004a0b216
A377811
E.g.f. satisfies A(x) = exp(x * A(x)) / (1 - x)^3.
[ "1", "4", "27", "283", "4217", "82971", "2041855", "60475885", "2096566449", "83324680435", "3736041351311", "186594364199277", "10274269171279657", "618386703880855339", "40393224245061185919", "2846030947359659421901", "215160957844217080056161", "17373449685399138641312739", "1492298627191467511376377999" ]
[ "nonn" ]
10
0
2
[ "A082030", "A352410", "A367789", "A377743", "A377810", "A377811" ]
null
Seiichi Manyama, Nov 08 2024
2025-02-16T08:34:07
oeisdata/seq/A377/A377811.seq
937990aabaa12ff486cbc2d2b8e12f61
A377812
Number of quadruples of positive integers (x,y,a,b) such that a < b, gcd(a,b) = gcd(x,y) = 1 and a*x + b*y = n.
[ "0", "0", "1", "2", "5", "4", "11", "9", "15", "12", "27", "14", "37", "22", "32", "31", "59", "26", "71", "38", "58", "48", "97", "42", "99", "62", "93", "68", "141", "48", "157", "91", "120", "94", "150", "78", "207", "112", "154", "108", "241", "84", "259", "138", "170", "150", "295", "116", "289", "144", "232", "178", "353", "136", "304", "188", "274", "210", "413", "132" ]
[ "nonn" ]
32
1
4
[ "A002133", "A274108", "A377812" ]
null
Anshveer Bindra, Nov 08 2024
2024-12-11T15:41:29
oeisdata/seq/A377/A377812.seq
8dab1b5572739159aa406465a6b9c874
A377813
Decimal expansion of arctanh(phi-1).
[ "7", "2", "1", "8", "1", "7", "7", "3", "7", "5", "8", "9", "4", "0", "5", "1", "7", "1", "2", "4", "6", "6", "3", "8", "3", "7", "0", "1", "3", "6", "5", "5", "2", "6", "3", "4", "7", "0", "2", "7", "7", "6", "5", "0", "1", "5", "7", "8", "4", "9", "0", "7", "7", "9", "4", "9", "1", "5", "2", "7", "2", "5", "3", "2", "6", "0", "2", "4", "5", "8", "0", "1", "4", "1", "2", "3", "3" ]
[ "nonn", "cons" ]
21
0
1
[ "A001622", "A202541", "A377813" ]
null
Colin Linzer, Nov 08 2024
2024-12-01T11:37:51
oeisdata/seq/A377/A377813.seq
c3423ed50203bb03ea9a3cd203353b20
A377814
Numbers k such that (37^k - 2^k)/35 is prime.
[ "3", "11", "43", "19963" ]
[ "nonn", "hard", "more" ]
6
1
1
[ "A062587", "A062589", "A127996", "A127997", "A128344", "A204940", "A217320", "A225807", "A229542", "A375161", "A375236", "A377031", "A377814" ]
null
Robert Price, Nov 08 2024
2025-02-16T08:34:07
oeisdata/seq/A377/A377814.seq
e5abe9a75dd69a02d59abb33db886942
A377815
Lexicographically earliest infinite sequence of distinct positive integers such that the binary concatenation of its terms yields the same string as the binary concatenation of the binary weights of its terms.
[ "1", "5", "2", "3", "4", "8", "15", "255", "7", "11", "13", "14", "16", "19", "21", "22", "6", "25", "32", "9", "26", "63", "65535", "23", "28", "10", "12", "64", "17", "95", "111", "128", "27", "256", "4294967295", "29", "35", "18", "20", "37", "38", "41", "42", "44", "49", "50", "52", "56", "67", "69", "24", "70", "73", "512", "30", "33", "31", "39", "18446744073709551615" ]
[ "nonn", "base" ]
21
1
2
[ "A302656", "A377815" ]
null
Dominic McCarty, Nov 08 2024
2024-11-17T07:35:12
oeisdata/seq/A377/A377815.seq
abd79390815a21b2ebd2e28dea0f9df4
A377816
Numbers that have a single even exponent in their prime factorization.
[ "4", "9", "12", "16", "18", "20", "25", "28", "44", "45", "48", "49", "50", "52", "60", "63", "64", "68", "72", "75", "76", "80", "81", "84", "90", "92", "98", "99", "108", "112", "116", "117", "121", "124", "126", "132", "140", "147", "148", "150", "153", "156", "162", "164", "169", "171", "172", "175", "176", "188", "192", "198", "200", "204", "207", "208", "212", "220", "228" ]
[ "nonn", "easy" ]
11
1
1
[ "A056798", "A065463", "A162645", "A229125", "A268335", "A350388", "A377816", "A377817", "A377818" ]
null
Amiram Eldar, Nov 09 2024
2024-11-09T08:01:04
oeisdata/seq/A377/A377816.seq
c035dcf5781ec2652cf181256f49b085
A377817
Numbers that have more than one even exponent in their prime factorization.
[ "36", "100", "144", "180", "196", "225", "252", "300", "324", "396", "400", "441", "450", "468", "484", "576", "588", "612", "676", "684", "700", "720", "784", "828", "882", "900", "980", "1008", "1044", "1089", "1100", "1116", "1156", "1200", "1225", "1260", "1296", "1300", "1332", "1444", "1452", "1476", "1521", "1548", "1575", "1584", "1600", "1620", "1692", "1700", "1764", "1800" ]
[ "nonn", "easy" ]
11
1
1
[ "A062312", "A072413", "A162645", "A268335", "A350388", "A377816", "A377817" ]
null
Amiram Eldar, Nov 09 2024
2024-11-09T08:26:44
oeisdata/seq/A377/A377817.seq
46e8b2a7c297f3a0dc6ffbaa267022d0
A377818
Powerful numbers that have a single even exponent in their prime factorization.
[ "4", "9", "16", "25", "49", "64", "72", "81", "108", "121", "169", "200", "256", "288", "289", "361", "392", "432", "500", "529", "625", "648", "675", "729", "800", "841", "961", "968", "972", "1024", "1125", "1152", "1323", "1352", "1369", "1372", "1568", "1681", "1728", "1849", "2000", "2209", "2312", "2401", "2592", "2809", "2888", "3087", "3200", "3267", "3481" ]
[ "nonn", "easy" ]
12
1
1
[ "A001694", "A056798", "A065487", "A335988", "A350388", "A377816", "A377818", "A377819" ]
null
Amiram Eldar, Nov 09 2024
2024-11-09T16:17:59
oeisdata/seq/A377/A377818.seq
b991cdb14e834f4f5c6cde51167fc417
A377819
Powerful numbers that have no more than one even exponent in their prime factorization.
[ "1", "4", "8", "9", "16", "25", "27", "32", "49", "64", "72", "81", "108", "121", "125", "128", "169", "200", "216", "243", "256", "288", "289", "343", "361", "392", "432", "500", "512", "529", "625", "648", "675", "729", "800", "841", "864", "961", "968", "972", "1000", "1024", "1125", "1152", "1323", "1331", "1352", "1369", "1372", "1568", "1681", "1728", "1849", "1944", "2000" ]
[ "nonn", "easy" ]
12
1
2
[ "A001694", "A056798", "A065487", "A335988", "A350388", "A377817", "A377818", "A377819" ]
null
Amiram Eldar, Nov 09 2024
2024-11-09T16:17:47
oeisdata/seq/A377/A377819.seq
2add0ff844a17ec141013936534e5c08
A377820
Powerful numbers that have a single odd exponent in their prime factorization.
[ "8", "27", "32", "72", "108", "125", "128", "200", "243", "288", "343", "392", "432", "500", "512", "648", "675", "800", "968", "972", "1125", "1152", "1323", "1331", "1352", "1372", "1568", "1728", "1800", "2000", "2048", "2187", "2197", "2312", "2592", "2700", "2888", "3087", "3125", "3200", "3267", "3528", "3872", "3888", "4232", "4500", "4563", "4608", "4913", "5000" ]
[ "nonn", "easy" ]
12
1
1
[ "A000037", "A001694", "A013661", "A085541", "A229125", "A246551", "A350389", "A370786", "A377820", "A377821" ]
null
Amiram Eldar, Nov 09 2024
2024-11-09T16:17:33
oeisdata/seq/A377/A377820.seq
3d7e30779668f4efc923d90c8578c76b
A377821
Powerful numbers that have no more than one odd exponent in their prime factorization.
[ "1", "4", "8", "9", "16", "25", "27", "32", "36", "49", "64", "72", "81", "100", "108", "121", "125", "128", "144", "169", "196", "200", "225", "243", "256", "288", "289", "324", "343", "361", "392", "400", "432", "441", "484", "500", "512", "529", "576", "625", "648", "675", "676", "729", "784", "800", "841", "900", "961", "968", "972", "1024", "1089", "1125", "1152" ]
[ "nonn", "easy" ]
12
1
2
[ "A000290", "A013661", "A085541", "A246551", "A350389", "A377820", "A377821" ]
null
Amiram Eldar, Nov 09 2024
2024-11-09T16:18:12
oeisdata/seq/A377/A377821.seq
235880914f8edc96b876035ac9a15ac8
A377822
a(n) is the least q>0 such that abs(p^2/q^2 - n)<=1/4 for a suitable integer p.
[ "1", "1", "2", "3", "1", "4", "2", "3", "5", "1", "5", "3", "2", "5", "4", "7", "1", "7", "4", "3", "2", "5", "3", "5", "8", "1", "9", "5", "7", "5", "2", "7", "3", "4", "6", "10", "1", "10", "6", "4", "3", "5", "2", "7", "8", "7", "5", "7", "12", "1", "12", "7", "5", "7", "3", "5", "2", "9", "5", "3", "4", "5", "8", "13", "1", "13", "8", "5", "4", "10", "8", "7", "2", "9", "5", "3", "7", "9", "6", "8", "15", "1", "15", "9", "6", "9", "7", "3", "8", "7", "2" ]
[ "nonn" ]
21
0
3
[ "A002522", "A377822" ]
null
Eric M. Hillman, Nov 08 2024
2025-03-24T09:26:20
oeisdata/seq/A377/A377822.seq
cf5230256b5617dbc2965b680c2a6bcd
A377823
Sum of the positions of maximum parts in all compositions of n.
[ "0", "1", "4", "10", "23", "50", "110", "240", "526", "1147", "2489", "5368", "11510", "24543", "52090", "110109", "231959", "487245", "1020980", "2134838", "4455582", "9283742", "19314740", "40128699", "83265342", "172564435", "357228078", "738707908", "1526004117", "3149310585", "6493394292", "13376521031", "27532616663" ]
[ "nonn", "easy" ]
17
0
3
[ "A001792", "A010054", "A011782", "A097976", "A097979", "A377823", "A377824" ]
null
John Tyler Rascoe, Nov 08 2024
2024-11-21T09:04:11
oeisdata/seq/A377/A377823.seq
54e05ff1d946237a92fc60f2b18534bd
A377824
Sum of the positions of minimum parts in all compositions of n.
[ "0", "1", "4", "10", "29", "70", "181", "435", "1046", "2470", "5762", "13283", "30371", "68847", "154935", "346433", "770154", "1703152", "3748574", "8214805", "17931172", "38997819", "84531066", "182661514", "393578129", "845777569", "1813017039", "3877390908", "8274351482", "17621535902", "37456091552", "79472869966" ]
[ "nonn", "easy" ]
28
0
3
[ "A001792", "A010054", "A011782", "A097976", "A097979", "A377823", "A377824" ]
null
John Tyler Rascoe, Nov 08 2024
2025-04-19T08:48:50
oeisdata/seq/A377/A377824.seq
641b8bb0cdac55f19d4ca5165694c048
A377825
Number of distinct permutations of the terms of the n-th row of Pascal's triangle with alternating signs.
[ "1", "2", "3", "24", "30", "720", "630", "40320", "22680", "3628800", "1247400", "479001600", "97297200", "87178291200", "10216206000", "20922789888000", "1389404016000", "6402373705728000", "237588086736000", "2432902008176640000", "49893498214560000", "1124000727777607680000", "12623055048283680000" ]
[ "nonn", "easy" ]
32
0
2
[ "A007019", "A007318", "A010050", "A072345", "A142150", "A377825" ]
null
Ryan Jean, Nov 08 2024
2024-12-25T04:26:52
oeisdata/seq/A377/A377825.seq
247977767166506890f56aa0cb620d2b
A377826
E.g.f. satisfies A(x) = (1 + x) * exp(x * A(x)).
[ "1", "2", "7", "49", "489", "6521", "108643", "2178107", "51084337", "1373054833", "41624314371", "1405311853595", "52299954524953", "2127347522554073", "93902399411048803", "4470613587492385051", "228362858274694209249", "12458393118650371672673", "722983769486947261178371" ]
[ "nonn" ]
11
0
2
[ "A352410", "A362771", "A377826", "A377827", "A377828" ]
null
Seiichi Manyama, Nov 09 2024
2025-02-16T08:34:07
oeisdata/seq/A377/A377826.seq
2e0f15eefc7afc39f41e58576f0e9662
A377827
E.g.f. satisfies A(x) = (1 + x)^2 * exp(x * A(x)).
[ "1", "3", "13", "106", "1273", "20226", "402589", "9637902", "269967793", "8666441650", "313793596981", "12653878751526", "562489374836041", "27328756018660266", "1440892788988703821", "81940739770677315646", "4999648556871348611425", "325806859913842861709922", "22584652022005415601772645" ]
[ "nonn" ]
13
0
2
[ "A362772", "A377740", "A377810", "A377826", "A377827", "A377828" ]
null
Seiichi Manyama, Nov 09 2024
2025-02-16T08:34:07
oeisdata/seq/A377/A377827.seq
5282949f446d830ca2c184c0d70439a6
A377828
E.g.f. satisfies A(x) = (1 + x)^3 * exp(x * A(x)).
[ "1", "4", "21", "193", "2669", "48711", "1113325", "30615019", "984983193", "36319515355", "1510538562641", "69968975169567", "3572684914283941", "199389519518767111", "12075888110164192917", "788850329621989132771", "55289606764547108653361", "4138807268239824817387443", "329564746571982961088975257" ]
[ "nonn" ]
11
0
2
[ "A377741", "A377811", "A377826", "A377827", "A377828" ]
null
Seiichi Manyama, Nov 09 2024
2025-02-16T08:34:07
oeisdata/seq/A377/A377828.seq
3502a9f8d0d99f5e0f1826d9e70a00ea
A377829
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x)/(1 + x)^2 ).
[ "1", "3", "25", "364", "7713", "216216", "7568041", "318256800", "15644919681", "880848974080", "55912403743161", "3951344780946432", "307737594185310625", "26190457718737019904", "2418475248758250599625", "240846113359411822759936", "25731326615411044591298049", "2935802801104074173428531200" ]
[ "nonn" ]
11
0
2
[ "A088690", "A377827", "A377829", "A377830" ]
null
Seiichi Manyama, Nov 09 2024
2024-11-09T08:01:09
oeisdata/seq/A377/A377829.seq
4cb966ee7dc2298f1f7e1ad21fdf8fe1
A377830
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x)/(1 + x)^3 ).
[ "1", "4", "45", "886", "25397", "963216", "45615553", "2595412240", "172624541769", "13150155923200", "1129371806449301", "107987110491257856", "11379014255782146685", "1310277285293012678656", "163703077517048727256425", "22057132253723442887059456", "3188342874266180285119069457", "492178313447920665621400780800" ]
[ "nonn" ]
10
0
2
[ "A088690", "A377829", "A377830" ]
null
Seiichi Manyama, Nov 09 2024
2024-11-09T08:10:54
oeisdata/seq/A377/A377830.seq
9dc618398ba6b87349b4ee5fa08031bd
A377831
Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x) * exp(-x) ).
[ "1", "2", "13", "154", "2701", "63216", "1856569", "65711024", "2724349401", "129552751360", "6952877604421", "415770771875328", "27416031835737637", "1976460653044957184", "154658036515292528625", "13055394531339601033216", "1182611605875201470044081", "114426900236922150187892736" ]
[ "nonn" ]
13
0
2
[ "A001622", "A377831", "A377832", "A377833" ]
null
Seiichi Manyama, Nov 09 2024
2025-04-02T07:20:42
oeisdata/seq/A377/A377831.seq
133fa1437f948623f8acb829207b65db
A377832
Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x)^2 * exp(-x) ).
[ "1", "3", "29", "508", "13137", "452616", "19549021", "1016932512", "61940154177", "4325943203200", "340900244374461", "29927648769380352", "2896829645184711121", "306522175683831195648", "35201889560564096132925", "4360880891670519541927936", "579686447990401730151243009", "82304944815106131595482267648" ]
[ "nonn" ]
11
0
2
[ "A377742", "A377810", "A377831", "A377832", "A377833" ]
null
Seiichi Manyama, Nov 09 2024
2024-11-09T08:19:35
oeisdata/seq/A377/A377832.seq
02a2e7281a40513c7b3c41795322bef6
A377833
Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x)^3 * exp(-x) ).
[ "1", "4", "51", "1174", "39833", "1799136", "101821723", "6938396368", "553482404721", "50619262481920", "5223014483031491", "600332651141435136", "76075005337204547209", "10538051760153093320704", "1584264031801742560408875", "256912816791069951740348416", "44703731640012047610981808097" ]
[ "nonn" ]
8
0
2
[ "A377743", "A377811", "A377831", "A377832", "A377833" ]
null
Seiichi Manyama, Nov 09 2024
2024-11-09T08:13:47
oeisdata/seq/A377/A377833.seq
7273df628633a325c3ac033e826e2cfd
A377834
a(1) = 0, and for n > 0, if A055932(n) = 2^r(1) * 3^r(2) * ... * prime(k)^r(k) with r(k) > 0 (where prime(k) denotes the k-th prime number), then the run lengths of the binary expansion of a(n) are (r(1), r(2), ..., r(k)).
[ "0", "1", "3", "2", "7", "6", "15", "4", "14", "5", "31", "12", "30", "8", "13", "63", "28", "9", "62", "24", "29", "127", "60", "11", "16", "25", "126", "10", "56", "61", "255", "17", "124", "27", "48", "57", "254", "26", "120", "19", "125", "32", "511", "49", "252", "59", "18", "112", "121", "23", "510", "33", "58", "248", "51", "253", "96", "1023", "22", "113", "508", "123", "50" ]
[ "nonn", "base" ]
7
1
3
[ "A005811", "A055932", "A124830", "A377834", "A377835", "A377836" ]
null
Rémy Sigrist, Nov 09 2024
2024-11-11T08:58:47
oeisdata/seq/A377/A377834.seq
1a6ce792a752915495249c5d31caf929
A377835
Inverse of bijection A377834.
[ "1", "2", "4", "3", "8", "10", "6", "5", "14", "18", "28", "24", "12", "15", "9", "7", "25", "32", "47", "40", "68", "83", "59", "50", "20", "26", "38", "34", "17", "21", "13", "11", "42", "52", "75", "65", "108", "129", "94", "81", "150", "179", "227", "213", "132", "157", "116", "99", "35", "44", "63", "55", "91", "111", "79", "69", "29", "36", "53", "46", "23", "30", "19", "16", "67" ]
[ "nonn", "base" ]
6
0
2
[ "A377834", "A377835" ]
null
Rémy Sigrist, Nov 09 2024
2024-11-11T08:58:34
oeisdata/seq/A377/A377835.seq
e442275ef89c2069dcc2b7796dc9694c
A377836
a(1) = 0, and for n > 0, if A055932(n) = 2^r(1) * 3^r(2) * ... * prime(k)^r(k) with r(k) > 0 (where prime(k) denotes the k-th prime number), then the run lengths of the binary expansion of a(n) are (r(k), r(k-1), ..., r(1)).
[ "0", "1", "3", "2", "7", "4", "15", "6", "8", "5", "31", "12", "16", "14", "11", "63", "24", "9", "32", "28", "23", "127", "48", "13", "30", "19", "64", "10", "56", "47", "255", "17", "96", "27", "60", "39", "128", "20", "112", "25", "95", "62", "511", "35", "192", "55", "22", "120", "79", "29", "256", "33", "40", "224", "51", "191", "124", "1023", "18", "71", "384", "111", "44", "240" ]
[ "nonn", "base" ]
6
1
3
[ "A005811", "A055932", "A124830", "A377834", "A377836", "A377837" ]
null
Rémy Sigrist, Nov 09 2024
2024-11-11T08:58:30
oeisdata/seq/A377/A377836.seq
980bd997405dfc080588b6723a7cd624
A377837
Inverse of bijection A377836.
[ "1", "2", "4", "3", "6", "10", "8", "5", "9", "18", "28", "15", "12", "24", "14", "7", "13", "32", "59", "26", "38", "83", "47", "21", "17", "40", "68", "34", "20", "50", "25", "11", "19", "52", "116", "44", "79", "179", "94", "36", "53", "129", "227", "111", "63", "157", "75", "30", "23", "65", "132", "55", "91", "213", "108", "46", "29", "81", "150", "69", "35", "99", "42", "16", "27" ]
[ "nonn", "base" ]
6
0
2
[ "A377836", "A377837" ]
null
Rémy Sigrist, Nov 09 2024
2024-11-11T08:58:25
oeisdata/seq/A377/A377837.seq
7a9286225d92649950b00293c66d0daa
A377838
Let p = prime(n), then a(n) is the least prime q < p such that p * q# + 1 is prime.
[ "2", "2", "3", "2", "3", "3", "5", "2", "2", "13", "3", "2", "5", "3", "2", "7", "3", "5", "5", "3", "5", "2", "2", "11", "3", "3", "3", "5", "2", "13", "2", "3", "7", "13", "3", "7", "7", "5", "2", "2", "3", "2", "5", "13", "11", "29", "5", "19", "5", "2", "2", "3", "2", "3", "3", "13", "3", "3", "2", "3", "2", "13", "3", "3", "5", "3", "5", "3", "7", "7", "2", "3", "3", "11", "5", "67", "3", "7", "17", "2", "7", "2", "7" ]
[ "nonn" ]
12
2
1
[ "A034386", "A377838" ]
null
Jeppe Stig Nielsen, Nov 09 2024
2024-11-13T18:29:00
oeisdata/seq/A377/A377838.seq
8b1b3694c49d059e28982c98bb4fa142
A377839
Numbers k such that (25^k - 2^k)/23 is prime.
[ "11", "199", "509", "857", "42841" ]
[ "nonn", "hard", "more" ]
6
1
1
[ "A062587", "A062589", "A127996", "A127997", "A128344", "A204940", "A217320", "A225807", "A229542", "A375161", "A375236", "A377031", "A377839" ]
null
Robert Price, Nov 09 2024
2025-02-16T08:34:07
oeisdata/seq/A377/A377839.seq
b4d9baf4ae1f6a83132a845b26eafd81
A377840
Cogrowth sequence of the 16-element group C8 X C2 = <S,T | S^8, T^2, [S,T]>.
[ "1", "1", "1", "1", "2", "46", "496", "3004", "12872", "43912", "130816", "394384", "1470944", "6874336", "33550336", "151869376", "622116992", "2353246336", "8589869056", "31961192704", "125858012672", "521796316672", "2199022206976", "9122012806144", "36758056208384", "144536687773696", "562949936644096" ]
[ "nonn", "easy" ]
8
0
5
[ "A007582", "A377627", "A377714", "A377840", "C2", "C4", "C6", "D8" ]
null
Sean A. Irvine, Nov 09 2024
2024-11-10T20:41:15
oeisdata/seq/A377/A377840.seq
beb15ab73f8068bbb8c56de92bfd3076
A377841
Index of first occurrence of n in A375277, or -1 if n does not appear there.
[ "1", "2", "13", "4", "8", "6", "37", "14", "49", "10", "20", "12", "1553", "26", "85", "16", "97", "18", "47", "32", "15114", "22", "44", "89", "145", "50", "54", "28", "56", "30", "33", "187", "31", "4073", "68", "36", "122", "91", "76", "40", "80", "42", "61", "86", "265", "46", "277", "94", "289", "98", "205", "52", "62", "1260", "337", "63", "971", "58", "349", "60", "288", "167", "84", "379", "128" ]
[ "base", "nonn" ]
25
1
2
[ "A000040", "A000142", "A375277", "A377841" ]
null
Robert G. Wilson v, Nov 10 2024
2024-12-10T10:15:09
oeisdata/seq/A377/A377841.seq
a063eca4cb53a1996e0d6deda20dae1e
A377842
a(n) = q - 2*p, where q is the greatest prime such that p=2*n - q is also prime.
[ "-2", "-3", "-1", "1", "-3", "5", "7", "3", "11", "13", "9", "17", "13", "9", "23", "25", "21", "17", "31", "27", "35", "37", "33", "41", "37", "33", "47", "43", "39", "53", "55", "51", "47", "61", "57", "65", "67", "63", "59", "73", "69", "77", "73", "69", "83", "79", "75", "41", "91", "87", "95", "97", "93", "101", "103", "99", "107", "103", "99", "83", "91", "87", "71", "121", "117", "125", "121", "117", "131", "133" ]
[ "sign" ]
27
2
1
[ "A020481", "A020482", "A377842", "A378896" ]
null
Michel Eduardo Beleza Yamagishi, Dec 10 2024
2024-12-16T14:30:14
oeisdata/seq/A377/A377842.seq
13f0244717d70d5aba845d88240d4acc
A377843
Cogrowth sequence of the 16-element group C4 X C2 X C2 = <S,T,U | S^4, T^2, U^2, [S,T], [S,U], [T,U]>.
[ "1", "2", "9", "62", "689", "7322", "69369", "616982", "5422049", "48197042", "433434729", "3913915502", "35311723409", "317999340362", "2860994944089", "25738114039622", "231602961592769", "2084457277181282", "18761300850805449", "168858054223133342", "1519730933499158129", "13677470410291063802" ]
[ "nonn", "easy" ]
17
0
2
[ "A007582", "A070775", "A377714", "A377840", "A377843", "C2", "C4", "C8", "D8" ]
null
Sean A. Irvine, Nov 09 2024
2024-11-10T20:43:52
oeisdata/seq/A377/A377843.seq
4af7f1fb09f74aa30c51c79307dfce9b
A377844
Numbers that have a single odd exponent larger than 1 in their prime factorization.
[ "8", "24", "27", "32", "40", "54", "56", "72", "88", "96", "104", "108", "120", "125", "128", "135", "136", "152", "160", "168", "184", "189", "200", "224", "232", "243", "248", "250", "264", "270", "280", "288", "296", "297", "312", "328", "343", "344", "351", "352", "360", "375", "376", "378", "384", "392", "408", "416", "424", "432", "440", "456", "459", "472", "480", "486", "488", "500" ]
[ "nonn", "easy" ]
9
1
1
[ "A060476", "A065036", "A065465", "A143610", "A163569", "A295661", "A325990", "A376142", "A377844", "A377845" ]
null
Amiram Eldar, Nov 09 2024
2024-11-10T05:03:59
oeisdata/seq/A377/A377844.seq
cc0131ce93e4b48da6a46add60546aa0
A377845
Numbers that have more than one odd exponent larger than 1 in their prime factorization.
[ "216", "864", "1000", "1080", "1512", "1944", "2376", "2744", "2808", "3000", "3375", "3456", "3672", "4000", "4104", "4320", "4968", "5400", "6048", "6264", "6696", "6750", "7000", "7560", "7776", "7992", "8232", "8856", "9000", "9261", "9288", "9504", "9720", "10152", "10584", "10648", "10976", "11000", "11232", "11448", "11880", "12000", "12744", "13000" ]
[ "nonn", "easy" ]
8
1
1
[ "A065465", "A162142", "A179671", "A190011", "A295661", "A335275", "A377844", "A377845" ]
null
Amiram Eldar, Nov 09 2024
2024-11-10T05:06:27
oeisdata/seq/A377/A377845.seq
6f36f1b351d47edf1ea8574ff75abe25
A377846
Powerful numbers that are not divisible by the cubes of more than one distinct prime.
[ "1", "4", "8", "9", "16", "25", "27", "32", "36", "49", "64", "72", "81", "100", "108", "121", "125", "128", "144", "169", "196", "200", "225", "243", "256", "288", "289", "324", "343", "361", "392", "400", "441", "484", "500", "512", "529", "576", "625", "675", "676", "729", "784", "800", "841", "900", "961", "968", "972", "1024", "1089", "1125", "1152", "1156", "1225" ]
[ "nonn", "easy" ]
9
1
2
[ "A001694", "A082020", "A143610", "A376936", "A377821", "A377846", "A377847" ]
null
Amiram Eldar, Nov 09 2024
2024-11-10T05:38:48
oeisdata/seq/A377/A377846.seq
60d1961502593ec641c25198a6b96965
A377847
Powerful numbers that are divisible by the cube of a single prime.
[ "8", "16", "27", "32", "64", "72", "81", "108", "125", "128", "144", "200", "243", "256", "288", "324", "343", "392", "400", "500", "512", "576", "625", "675", "729", "784", "800", "968", "972", "1024", "1125", "1152", "1323", "1331", "1352", "1372", "1568", "1600", "1800", "1936", "2025", "2048", "2187", "2197", "2304", "2312", "2401", "2500", "2700", "2704", "2888", "2916" ]
[ "nonn", "easy" ]
12
1
1
[ "A001694", "A030078", "A082020", "A320966", "A377846", "A377847" ]
null
Amiram Eldar, Nov 09 2024
2025-03-31T01:45:36
oeisdata/seq/A377/A377847.seq
c02c5c2f6eddac7cf4831ce113976312
A377848
Even numbers which are the sum of two palindromic primes.
[ "4", "6", "8", "10", "12", "14", "16", "18", "22", "104", "106", "108", "112", "134", "136", "138", "142", "154", "156", "158", "162", "184", "186", "188", "192", "194", "196", "198", "202", "232", "252", "262", "282", "292", "302", "312", "316", "318", "320", "322", "324", "332", "342", "356", "358", "360", "362", "364", "372", "376", "378", "380", "382", "384", "386" ]
[ "nonn", "base" ]
31
1
1
[ "A002385", "A005843", "A287961", "A377848", "A379138" ]
null
James S. DeArmon, Nov 09 2024
2025-06-02T18:26:16
oeisdata/seq/A377/A377848.seq
d04ed59102dda3cbf3013ace9afedb30
A377849
Decimal expansion of the real root of x^3 + 2*x^2 - phi^2, where phi is the golden ratio (A001622).
[ "9", "4", "3", "1", "5", "1", "2", "5", "9", "2", "4", "3", "8", "8", "1", "8", "1", "7", "1", "2", "6", "7", "1", "9", "8", "9", "2", "5", "7", "0", "3", "6", "4", "1", "5", "9", "4", "0", "6", "6", "5", "0", "3", "8", "6", "2", "3", "4", "5", "3", "4", "7", "0", "4", "6", "0", "4", "8", "9", "1", "2", "8", "5", "3", "9", "0", "3", "3", "6", "0", "8", "4", "8", "5", "9", "4", "9", "1", "8", "4", "4", "7", "4", "6", "7", "4", "4", "0", "9", "0" ]
[ "nonn", "cons", "easy" ]
14
0
1
[ "A001622", "A377805", "A377806", "A377807", "A377849" ]
null
Paolo Xausa, Nov 09 2024
2025-02-10T08:41:11
oeisdata/seq/A377/A377849.seq
8bce70db62b15d0875afcd366a2deba6
A377850
Noll index series of Zernike polynomials converted to Fringe index.
[ "1", "2", "3", "4", "6", "5", "8", "7", "11", "10", "9", "12", "13", "17", "18", "14", "15", "19", "20", "26", "27", "16", "22", "21", "29", "28", "38", "37", "24", "23", "31", "30", "40", "39", "51", "50", "25", "32", "33", "41", "42", "52", "53", "65", "66", "34", "35", "43", "44", "54", "55", "67", "68", "82", "83", "36", "46", "45", "57", "56", "70", "69", "85", "84", "102", "101", "48", "47", "59", "58", "72", "71", "87", "86" ]
[ "nonn", "easy" ]
26
1
2
[ "A176988", "A375510", "A377850" ]
null
Gerhard Ramsebner, Nov 09 2024
2025-04-02T04:43:51
oeisdata/seq/A377/A377850.seq
77aac0a089e1b961bfeba3f040f49127
A377851
Smallest multiplier which can complete the square for n-polygonal numbers, together with a constant offset.
[ "8", "1", "24", "8", "40", "3", "56", "16", "72", "5", "88", "24", "104", "7", "120", "32", "136", "9", "152", "40", "168", "11", "184", "48", "200", "13", "216", "56", "232", "15", "248", "64", "264", "17", "280", "72", "296", "19", "312", "80", "328", "21", "344", "88", "360", "23", "376", "96", "392", "25", "408", "104", "424", "27", "440", "112", "456", "29", "472" ]
[ "nonn", "easy" ]
45
3
1
[ "A181318", "A377851" ]
null
Jonathan Dushoff, Nov 09 2024
2024-12-07T14:57:16
oeisdata/seq/A377/A377851.seq
383f84e22b8a59555e34d118397278a0
A377852
Triangle T(n,k) read by rows in which n-th row lists in increasing order all multiplicative partitions mu of n whose sum is also n (with factors >= 1), encoded as Product_{j in mu} prime(j); n>=1, 1<=k<=A001055(n).
[ "2", "3", "5", "7", "9", "11", "13", "30", "17", "19", "84", "108", "23", "200", "29", "264", "31", "37", "624", "1120", "1440", "41", "43", "1632", "47", "7040", "53", "3648", "12544", "16128", "20736", "59", "61", "8832", "33280", "76800", "67", "71", "22272", "157696", "202752", "73", "174080", "79", "47616", "83", "89", "113664", "778240", "1490944", "1916928", "3440640", "4423680" ]
[ "nonn", "tabf" ]
17
1
1
[ "A000040", "A001055", "A215366", "A377852", "A377853", "A378175" ]
null
Alois P. Heinz, Nov 09 2024
2024-11-21T05:33:33
oeisdata/seq/A377/A377852.seq
6d8c114374a264a3d49c244d6a539e42
A377853
Sum over all multiplicative partitions mu of n whose sum is also n (with factors >= 1), of the encoding as Product_{j in mu} prime(j).
[ "2", "3", "5", "16", "11", "43", "17", "211", "223", "293", "31", "3221", "41", "1675", "7087", "53109", "59", "118973", "67", "382791", "174153", "47695", "83", "12164185", "3965025", "252005", "36536423", "36180075", "109", "268148849", "127", "2749874307", "81264777", "5800075", "1568669845", "39708983447", "157", "26345635", "1719664807" ]
[ "nonn" ]
13
1
1
[ "A000040", "A006450", "A377852", "A377853", "A378176" ]
null
Alois P. Heinz, Nov 09 2024
2024-11-20T05:18:46
oeisdata/seq/A377/A377853.seq
72a3123c3e36ad6ef78e8eba6fdaeeda
A377854
Achilles numbers whose squarefree kernel is a primorial.
[ "72", "108", "288", "432", "648", "864", "972", "1152", "1800", "1944", "2592", "2700", "3456", "3888", "4500", "4608", "5400", "6912", "7200", "8748", "9000", "10368", "10800", "13500", "15552", "16200", "17496", "18000", "18432", "21600", "23328", "24300", "27648", "28800", "31104", "34992", "36000", "40500", "41472", "43200", "45000", "48600" ]
[ "nonn", "easy" ]
45
1
1
[ "A001597", "A001694", "A002110", "A007947", "A052486", "A055932", "A286708", "A369374", "A377854", "A378002" ]
null
Michael De Vlieger, Nov 16 2024
2024-11-17T07:09:36
oeisdata/seq/A377/A377854.seq
c58f5d1169021602665fa59f288674f8
A377855
Cogrowth sequence of the 16-element group C4:C4 = <S,T | S^4, T^4, STST^3>.
[ "1", "0", "2", "6", "40", "120", "512", "2016", "8320", "32640", "131072", "523776", "2099200", "8386560", "33554432", "134209536", "536903680", "2147450880", "8589934592", "34359607296", "137439477760", "549755289600", "2199023255552", "8796090925056", "35184380477440", "140737479966720", "562949953421312" ]
[ "nonn", "easy" ]
8
0
3
[ "A070775", "A377840", "A377855", "C2", "C4", "C8" ]
null
Sean A. Irvine, Nov 09 2024
2024-11-13T15:33:40
oeisdata/seq/A377/A377855.seq
5eb5f29cd112afb7e544dcebd52a5a5c
A377856
Numbers k such that (21^k + 2^k)/23 is prime.
[ "11", "17", "47", "2663" ]
[ "nonn", "hard", "more" ]
6
1
1
[ "A057187", "A057188", "A062587", "A062589", "A127996", "A127997", "A128344", "A204940", "A217320", "A225807", "A228922", "A229542", "A375161", "A375236", "A377031", "A377856" ]
null
Robert Price, Nov 09 2024
2025-02-16T08:34:07
oeisdata/seq/A377/A377856.seq
36bc18966025d27c0f77a9d6fb24c889
A377857
Number of subwords of the form UUUD in nondecreasing Dyck paths of length 2n.
[ "0", "0", "0", "1", "5", "18", "60", "191", "589", "1775", "5257", "15360", "44394", "127171", "361595", "1021693", "2871245", "8031246", "22372344", "62096135", "171797257", "473928875", "1304007889", "3579517116", "9804791910", "26804181643", "73145473655", "199276078201", "542076556949", "1472491141770", "3994615719732" ]
[ "nonn", "easy" ]
22
0
5
[ "A000032", "A000045", "A375995", "A377670", "A377679", "A377857" ]
null
Rigoberto Florez, Nov 09 2024
2025-03-04T08:35:56
oeisdata/seq/A377/A377857.seq
247b7d0f623a99fb85c37cb9837f2060
A377858
a(n) = Sum_{k=1..n} tan(k*Pi/(1+2*n))^4.
[ "0", "9", "90", "371", "1044", "2365", "4654", "8295", "13736", "21489", "32130", "46299", "64700", "88101", "117334", "153295", "196944", "249305", "311466", "384579", "469860", "568589", "682110", "811831", "959224", "1125825", "1313234", "1523115", "1757196", "2017269", "2305190", "2622879", "2972320", "3355561", "3774714" ]
[ "nonn", "easy" ]
34
0
2
[ "A014105", "A376777", "A377858" ]
null
Seiichi Manyama, Nov 09 2024
2024-11-11T09:01:44
oeisdata/seq/A377/A377858.seq
64d206b94cf09f1d08dc44b10d4df4fa
A377859
Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x) * exp(x) ).
[ "1", "0", "1", "2", "21", "144", "1765", "21552", "340137", "5845760", "116495721", "2550320640", "62023290109", "1642735460352", "47321500546125", "1469008742856704", "48962556079079505", "1742660440701861888", "65993849612007279697", "2648999558505185280000", "112360563741545020804581" ]
[ "nonn" ]
10
0
4
[ "A377831", "A377859", "A377860", "A377861" ]
null
Seiichi Manyama, Nov 09 2024
2024-11-10T03:34:55
oeisdata/seq/A377/A377859.seq
427a6c889d1a5d0dfcf7b6b192ca3f34
A377860
Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x)^2 * exp(x) ).
[ "1", "1", "5", "44", "577", "10104", "222133", "5886880", "182775969", "6509571200", "261665344261", "11720054882304", "578878362625825", "31259890045425664", "1832295378792935925", "115862322601669627904", "7861907382202262095297", "569837358810005613281280", "43939338917141224534941829" ]
[ "nonn" ]
9
0
3
[ "A377832", "A377859", "A377860", "A377861" ]
null
Seiichi Manyama, Nov 09 2024
2024-11-10T05:02:11
oeisdata/seq/A377/A377860.seq
ed9b1f7402a984640c3274af5a9d563e
A377861
Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x)^3 * exp(x) ).
[ "1", "2", "15", "206", "4193", "113904", "3882511", "159475280", "7672503681", "423360926720", "26362968645071", "1829066086810368", "139929538526047585", "11703312997355442176", "1062423600515479191375", "104042389901715413633024", "10933256593926589800851969", "1227201235266954603172331520" ]
[ "nonn" ]
9
0
2
[ "A377833", "A377859", "A377860", "A377861" ]
null
Seiichi Manyama, Nov 09 2024
2024-11-10T05:01:10
oeisdata/seq/A377/A377861.seq
a856fc2d669ce36a0d0ae93ed5f13b79
A377862
A variant of Golomb's sequence (A001462): the n-th digit of the sequence gives the number of times n appears, with a(1) = 1 and a(2) = 2.
[ "1", "2", "2", "3", "3", "4", "4", "4", "5", "5", "5", "6", "6", "6", "6", "7", "7", "7", "7", "8", "8", "8", "8", "9", "9", "9", "9", "9", "10", "10", "10", "10", "10", "11", "11", "11", "11", "11", "12", "12", "12", "12", "12", "12", "13", "13", "13", "13", "13", "13", "14", "14", "14", "14", "14", "14", "15", "15", "15", "15", "15", "15", "16", "16", "16", "16", "16", "16", "16", "17", "17", "17", "17", "17", "17", "17", "18", "18", "18", "18", "18", "18", "18", "19", "19" ]
[ "nonn", "base" ]
11
1
2
[ "A001462", "A087739", "A167500", "A377862", "A377863", "A377896" ]
null
Rémy Sigrist, Nov 10 2024
2024-11-14T11:03:41
oeisdata/seq/A377/A377862.seq
9c927c8404ce65f225f6240029c23281
A377863
Numbers missing from A377862.
[ "30", "32", "34", "36", "38", "154", "156", "158", "160", "162", "164", "166", "168", "320", "340", "342", "370", "372", "408", "410", "412", "454", "456", "458", "460", "508", "510", "512", "514", "516", "570", "571", "573", "574", "576", "577", "579", "580", "582", "583", "585", "586", "588", "591", "594", "597", "600", "603", "606", "609", "612", "615", "618" ]
[ "nonn", "base" ]
7
1
1
[ "A377862", "A377863", "A377896" ]
null
Rémy Sigrist, Nov 10 2024
2024-11-11T12:03:56
oeisdata/seq/A377/A377863.seq
6e4676a4a7a17c0a0aa039028bf85fff
A377864
Largest divisor of 2n-1 less than or equal to sqrt(2n-1).
[ "1", "1", "1", "1", "3", "1", "1", "3", "1", "1", "3", "1", "5", "3", "1", "1", "3", "5", "1", "3", "1", "1", "5", "1", "7", "3", "1", "5", "3", "1", "1", "7", "5", "1", "3", "1", "1", "5", "7", "1", "9", "1", "5", "3", "1", "7", "3", "5", "1", "9", "1", "1", "7", "1", "1", "3", "1", "5", "9", "7", "11", "3", "5", "1", "3", "1", "7", "9", "1", "1", "3", "11", "5", "7", "1", "1", "9", "5", "1", "3", "7", "1", "11", "1", "13", "9" ]
[ "nonn", "easy" ]
16
1
5
[ "A033676", "A219695", "A377499", "A377864" ]
null
Charles Kusniec, Nov 10 2024
2024-11-21T09:06:20
oeisdata/seq/A377/A377864.seq
c5c6aea2b798bdaf81e9b941c97f4d2e
A377865
Smallest divisor of 2n-1 greater than or equal to sqrt(2n-1).
[ "1", "3", "5", "7", "3", "11", "13", "5", "17", "19", "7", "23", "5", "9", "29", "31", "11", "7", "37", "13", "41", "43", "9", "47", "7", "17", "53", "11", "19", "59", "61", "9", "13", "67", "23", "71", "73", "15", "11", "79", "9", "83", "17", "29", "89", "13", "31", "19", "97", "11", "101", "103", "15", "107", "109", "37", "113", "23", "13", "17", "11", "41", "25", "127", "43", "131", "19" ]
[ "nonn", "easy" ]
15
1
2
[ "A033677", "A219695", "A377499", "A377865" ]
null
Charles Kusniec, Nov 10 2024
2024-11-24T20:04:06
oeisdata/seq/A377/A377865.seq
cc54293a211f0ca01d81cff15a049f1c
A377866
Number of subwords of the form DUUD or DDUUD in nondecreasing Dyck paths of length 2n.
[ "0", "0", "0", "1", "5", "18", "59", "185", "564", "1685", "4957", "14406", "41455", "118321", "335400", "945193", "2650229", "7398330", "20573219", "57013865", "157517532", "433993661", "1192779085", "3270835566", "8950887895", "24448816993", "66665369424", "181489721425", "493361278949" ]
[ "nonn", "easy" ]
17
0
5
[ "A000032", "A000045", "A375995", "A377670", "A377679", "A377866" ]
null
Rigoberto Florez, Nov 10 2024
2025-03-04T08:36:13
oeisdata/seq/A377/A377866.seq
45a06531e934783a859cfbc46c147be4
A377867
Number of subwords of the form DDDD in nondecreasing Dyck paths of length 2n.
[ "0", "0", "0", "0", "1", "7", "33", "131", "473", "1608", "5242", "16567", "51123", "154793", "461525", "1358646", "3957088", "11420995", "32707809", "93040751", "263113505", "740238852", "2073098086", "5782387855", "16070206191", "44516728277", "122956408493", "338707969266", "930787894348", "2552224341403", "6984100641117" ]
[ "nonn", "easy" ]
13
0
6
[ "A000032", "A000045", "A375995", "A377670", "A377679", "A377867" ]
null
Rigoberto Florez, Nov 10 2024
2025-03-04T08:36:24
oeisdata/seq/A377/A377867.seq
372451eaadb191d0161ec6df13393071
A377868
a(n) = A359550(A276085(n)), where A359550 is multiplicative with a(p^e) = 1 if p > e, otherwise 0, and A276085 is fully additive with a(p) = p#/p.
[ "0", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "1", "0", "1", "1", "0", "1", "1", "1", "1", "0", "1", "0", "1", "1", "1", "0", "1", "1", "1", "1", "0", "1", "1", "1", "1", "0", "1", "0", "0", "1", "1", "0", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "0", "0", "1", "1", "1", "1", "1", "1", "0", "0", "1", "1", "1", "0", "1", "1", "1", "0", "1", "0", "1", "1", "1", "0", "0", "0", "1", "0", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "1", "0", "0", "1", "1", "0", "1", "0" ]
[ "nonn" ]
27
1
null
[ "A276085", "A359550", "A369001", "A377868", "A377869", "A377870", "A377874", "A377875" ]
null
Antti Karttunen, Nov 10 2024
2024-11-17T13:07:05
oeisdata/seq/A377/A377868.seq
ddf1ff8ff4ba9425ddc8d8cad8220e41
A377869
Numbers k such that A276085(k) has no divisors of the form p^p, where A276085 is fully additive with a(p) = p#/p.
[ "2", "3", "4", "5", "6", "7", "8", "10", "11", "13", "14", "17", "18", "19", "22", "23", "24", "26", "27", "29", "30", "31", "32", "34", "36", "37", "38", "40", "41", "42", "43", "45", "46", "47", "48", "50", "53", "54", "56", "58", "59", "60", "61", "62", "63", "64", "66", "67", "70", "71", "72", "73", "74", "75", "78", "79", "80", "82", "83", "84", "86", "88", "89", "90", "94", "96", "97", "98", "99", "100", "101", "102", "103", "104", "105", "106", "107", "109" ]
[ "nonn" ]
29
1
1
[ "A000040", "A046315", "A048103", "A100484", "A276085", "A276086", "A369002", "A369003", "A377868", "A377869", "A377871", "A377872", "A377873", "A377875", "A377878", "A377989" ]
null
Antti Karttunen, Nov 10 2024
2024-11-19T17:24:10
oeisdata/seq/A377/A377869.seq
9bc395a8e03159b3818e4f3d65ee4688
A377870
a(n) = A359550(n) * A359550(A276085(n)), where A359550 is multiplicative with a(p^e) = 1 if p > e, otherwise 0, and A276085 is fully additive with a(p) = p#/p.
[ "0", "1", "1", "0", "1", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "1", "1", "0", "0", "1", "0", "0", "1", "1", "0", "0", "1", "1", "1", "0", "1", "1", "1", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "1", "1", "0", "1", "1", "1", "0", "0", "1", "1", "0", "0", "1", "1", "0", "1", "1", "1", "0", "0", "1", "1", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "0", "0", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "0", "0", "1", "1", "0", "0", "1", "1", "0", "0", "0" ]
[ "nonn" ]
8
1
null
[ "A276085", "A359550", "A377868", "A377870", "A377871" ]
null
Antti Karttunen, Nov 10 2024
2024-11-10T17:09:16
oeisdata/seq/A377/A377870.seq
bd702f8a887b652c38f0be5b63583f00
A377871
Numbers k such that neither k nor A276085(k) has divisors of the form p^p, where A276085 is fully additive with a(p) = p#/p.
[ "2", "3", "5", "6", "7", "10", "11", "13", "14", "17", "18", "19", "22", "23", "26", "29", "30", "31", "34", "37", "38", "41", "42", "43", "45", "46", "47", "50", "53", "58", "59", "61", "62", "63", "66", "67", "70", "71", "73", "74", "75", "78", "79", "82", "83", "86", "89", "90", "94", "97", "98", "99", "101", "102", "103", "105", "106", "107", "109", "110", "113", "114", "117", "118", "122", "125", "126", "127", "130", "131", "134", "137", "138", "139", "142" ]
[ "nonn" ]
19
1
1
[ "A000040", "A006862", "A048103", "A100484", "A143293", "A276086", "A276087", "A276092", "A376416", "A377869", "A377870", "A377871" ]
null
Antti Karttunen, Nov 10 2024
2024-11-19T17:24:15
oeisdata/seq/A377/A377871.seq
fa84ce60e348feda5fad3f116d8b4b5a
A377872
Numbers k for which A276085(k) is a multiple of 27, where A276085 is fully additive with a(p) = p#/p.
[ "1", "55", "95", "115", "155", "174", "187", "203", "232", "265", "282", "297", "323", "325", "329", "335", "376", "391", "396", "438", "462", "474", "511", "513", "515", "527", "528", "539", "553", "584", "606", "616", "621", "632", "649", "654", "678", "684", "704", "707", "745", "763", "791", "798", "808", "828", "837", "872", "901", "904", "906", "912", "913", "931", "966", "978", "1002", "1057", "1064", "1073", "1074", "1075", "1104", "1105" ]
[ "nonn" ]
44
1
2
[ "A276085", "A339746", "A369007", "A377869", "A377872", "A377873", "A377875", "A377876", "A377878" ]
null
Antti Karttunen, Nov 10 2024
2024-11-17T13:07:10
oeisdata/seq/A377/A377872.seq
2668443afd3544b4b8bf90025b58350b
A377873
Numbers k such that A276085(k) has at least one divisor of the form p^p, where A276085 is fully additive with a(p) = p#/p.
[ "1", "9", "12", "15", "16", "20", "21", "25", "28", "33", "35", "39", "44", "49", "51", "52", "55", "57", "65", "68", "69", "76", "77", "81", "85", "87", "91", "92", "93", "95", "108", "111", "115", "116", "119", "121", "123", "124", "129", "133", "135", "141", "143", "144", "145", "148", "155", "159", "161", "164", "169", "172", "174", "177", "180", "183", "185", "187", "188", "189", "192", "201", "203", "205", "209", "212", "213", "215", "217", "219" ]
[ "nonn" ]
8
1
2
[ "A100716", "A276085", "A369002", "A377868", "A377869", "A377872", "A377873" ]
null
Antti Karttunen, Nov 10 2024
2024-11-10T21:46:18
oeisdata/seq/A377/A377873.seq
5eba3382fc1eeead6c12d84822f0137d
A377874
Parity of A083345(n), where A083345(n) = n' / gcd(n,n') = numerator of Sum(e/p: n=Product(p^e)).
[ "0", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "1", "0", "1", "1", "0", "1", "1", "1", "1", "0", "1", "0", "1", "1", "1", "0", "1", "1", "1", "1", "0", "1", "1", "1", "1", "0", "1", "0", "0", "1", "1", "0", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "0", "0", "1", "1", "1", "1", "1", "1", "0", "0", "1", "1", "1", "0", "1", "1", "1", "0", "1", "0", "1", "1", "1", "0", "0", "0", "1", "0", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "1", "0", "0", "1", "1", "0", "1", "0" ]
[ "nonn", "easy" ]
14
1
null
[ "A000035", "A083345", "A165560", "A166486", "A276085", "A369001", "A369002", "A369003", "A369980", "A377868", "A377874", "A377875" ]
null
Antti Karttunen, Nov 11 2024
2024-11-11T10:21:32
oeisdata/seq/A377/A377874.seq
f345bf4369c19dfdd260398dca8770a6
A377875
Numbers k for which A276085(k) is not a multiple of 4 and has at least one divisor of the form p^p, with p an odd prime, where A276085 is fully additive with a(p) = p#/p.
[ "174", "232", "282", "325", "376", "438", "462", "474", "539", "584", "606", "616", "632", "654", "678", "798", "808", "872", "904", "906", "931", "966", "978", "1002", "1064", "1074", "1075", "1105", "1127", "1182", "1208", "1288", "1302", "1304", "1336", "1398", "1432", "1506", "1519", "1576", "1626", "1662", "1736", "1755", "1842", "1864", "1866", "2008", "2168", "2216", "2226", "2340", "2425", "2442", "2456", "2488", "2514" ]
[ "nonn" ]
23
1
1
[ "A083345", "A276085", "A369002", "A369003", "A377868", "A377869", "A377872", "A377873", "A377874", "A377875" ]
null
Antti Karttunen, Nov 11 2024
2024-11-13T08:28:28
oeisdata/seq/A377/A377875.seq
5bbf6802c0ce8e03bd6fe660d2db54cf
A377876
The n-th primorial number reduced modulo 27.
[ "1", "2", "6", "3", "21", "15", "6", "21", "21", "24", "21", "3", "3", "15", "24", "21", "6", "3", "21", "3", "24", "24", "6", "12", "15", "24", "21", "3", "24", "24", "12", "12", "6", "12", "21", "24", "6", "24", "24", "12", "24", "3", "3", "6", "24", "3", "3", "12", "3", "6", "24", "3", "15", "24", "3", "15", "3", "24", "24", "6", "12", "21", "24", "24", "12", "3", "6", "15", "6", "3", "21", "15", "12", "3", "12", "12", "6", "12", "12", "6", "24", "12", "3", "24", "24", "6", "12", "15" ]
[ "nonn" ]
15
0
2
[ "A002110", "A086360", "A377872", "A377876", "A377877" ]
null
Antti Karttunen, Nov 12 2024
2024-11-13T17:16:35
oeisdata/seq/A377/A377876.seq
d712daaa2842513673849a55d94f8f8d
A377877
The n-th primorial number reduced modulo 3125.
[ "1", "2", "6", "30", "210", "2310", "1905", "1135", "2815", "2245", "2605", "2630", "435", "2210", "1280", "785", "980", "1570", "2020", "965", "2890", "1595", "1005", "2165", "2060", "2945", "570", "2460", "720", "355", "2615", "855", "2630", "935", "1840", "2285", "1285", "1745", "60", "645", "2210", "1840", "1790", "1265", "395", "2815", "810", "2160", "430", "735", "2690", "1770", "1155", "230", "1480", "2235", "305", "795" ]
[ "nonn", "less" ]
12
0
2
[ "A002110", "A086360", "A377876", "A377877" ]
null
Antti Karttunen, Nov 13 2024
2024-11-13T16:56:25
oeisdata/seq/A377/A377877.seq
06f7ce80e28b971a120b26fad92a950e
A377878
Numbers k for which A276085(k) is a multiple of 3125, where A276085 is fully additive with a(p) = p#/p.
[ "1", "4823", "8267", "9553", "15623", "15833", "15929", "20633", "23393", "28417", "33079", "34027", "36941", "37129", "37939", "42599", "43249", "44431", "47291", "49374", "60097", "65832", "66323", "69287", "69749", "70613", "74063", "74281", "74333", "74999", "77231", "83881", "86191", "86551", "87776", "88727", "99683", "106481", "108673", "111366", "113922", "115729", "118517", "124841", "126054", "129337" ]
[ "nonn" ]
12
1
2
[ "A000720", "A276085", "A373140", "A377869", "A377872", "A377873", "A377877", "A377878" ]
null
Antti Karttunen, Nov 13 2024
2024-11-16T10:20:10
oeisdata/seq/A377/A377878.seq
764960149f22497105cee50df2adc831
A377879
Deficiency of squares: a(n) = 2n^2 - sigma(n^2).
[ "1", "1", "5", "1", "19", "-19", "41", "1", "41", "-17", "109", "-115", "155", "-7", "47", "1", "271", "-199", "341", "-161", "141", "37", "505", "-499", "469", "71", "365", "-199", "811", "-1021", "929", "1", "449", "163", "683", "-1159", "1331", "221", "663", "-737", "1639", "-1659", "1805", "-251", "299", "361", "2161", "-2035", "2001", "-467", "1211", "-265", "2755", "-1819", "1927", "-967", "1545", "631", "3421", "-5293", "3659", "737" ]
[ "sign" ]
15
1
3
[ "A000012", "A000079", "A000290", "A003961", "A033879", "A083064", "A083884", "A377879", "A378231" ]
null
Antti Karttunen, Nov 23 2024
2024-11-24T11:27:39
oeisdata/seq/A377/A377879.seq
2a24e9088f50288a46ea55ea47583dff
A377880
Nonprime cubefree numbers.
[ "1", "4", "6", "9", "10", "12", "14", "15", "18", "20", "21", "22", "25", "26", "28", "30", "33", "34", "35", "36", "38", "39", "42", "44", "45", "46", "49", "50", "51", "52", "55", "57", "58", "60", "62", "63", "65", "66", "68", "69", "70", "74", "75", "76", "77", "78", "82", "84", "85", "86", "87", "90", "91", "92", "93", "94", "95", "98", "99", "100", "102", "105", "106", "110", "111" ]
[ "nonn" ]
23
1
2
[ "A000469", "A004709", "A018252", "A377880" ]
null
Sahil K. Das, Nov 10 2024
2024-11-14T02:11:21
oeisdata/seq/A377/A377880.seq
cbc586161a8398645f16d00831a74409
A377881
Number of ordered pairs of real n X n (0,1)-matrices that satisfy the equation A + B = A * B.
[ "1", "1", "2", "72", "3760", "210042" ]
[ "nonn", "more" ]
23
0
3
[ "A060757", "A377881" ]
null
Stuart E Anderson, Nov 10 2024
2025-03-31T01:46:02
oeisdata/seq/A377/A377881.seq
b78482acb75c1b4e13c4bc64a822a81b
A377882
Numbers i for which A194627(i) is prime.
[ "2", "3", "9", "11", "29", "75", "77", "101", "105", "107", "221", "225", "235", "257", "315", "321", "323", "357", "363", "389", "411", "417", "431", "453", "455", "461", "501", "509", "515", "519", "557", "635", "645", "655", "689", "795", "799", "851", "885", "887", "911", "915", "921", "923", "933", "977", "989", "1029", "1033", "1037", "1071", "1073", "1145", "1167", "1175", "1187", "1197", "1201", "1241" ]
[ "nonn" ]
11
1
1
[ "A194627", "A377791", "A377882" ]
null
Robert Israel, Nov 10 2024
2024-11-12T22:19:21
oeisdata/seq/A377/A377882.seq
70ee0813afa24d9256a4fe00134d10c2
A377883
Cogrowth sequence of the 16-element modular group M4(2) = <S,T | S^8, T^2, STS^3T>.
[ "1", "1", "1", "7", "34", "126", "496", "2052", "8264", "32776", "130816", "524272", "2098144", "8388576", "33550336", "134217792", "536887424", "2147483776", "8589869056", "34359738112", "137439215104", "549755813376", "2199022206976", "8796093023232", "35184376285184", "140737488357376", "562949936644096" ]
[ "nonn", "easy" ]
10
0
4
[ "A007582", "A377840", "A377855", "A377883", "A377885", "C2", "C4", "C8", "D16", "D8" ]
null
Sean A. Irvine, Nov 10 2024
2024-11-11T05:50:57
oeisdata/seq/A377/A377883.seq
a9699405d4f047230965d00c46c9281d
A377884
Composite numbers k without prime factors that are divisors of the greatest primorial less than k.
[ "25", "49", "77", "91", "119", "121", "133", "143", "161", "169", "187", "203", "209", "221", "247", "253", "289", "299", "319", "323", "341", "361", "377", "391", "403", "407", "437", "451", "473", "481", "493", "517", "527", "529", "533", "551", "559", "583", "589", "611", "629", "649", "667", "671", "689", "697", "703", "713", "731", "737", "767", "779", "781", "793", "799" ]
[ "nonn" ]
26
1
1
[ "A002110", "A002808", "A260188", "A335284", "A377884" ]
null
Daniel D Gibson, Nov 10 2024
2024-12-12T23:32:55
oeisdata/seq/A377/A377884.seq
d5a32da18a1462b1e030af71d5739b1d
A377885
Cogrowth sequence of the 16-element quasihedral group SD16 = <S,T | S^8, T^2, STS^5T>.
[ "1", "1", "1", "4", "28", "136", "544", "2080", "8128", "32512", "130816", "524800", "2099200", "8390656", "33550336", "134201344", "536854528", "2147516416", "8590065664", "34359869440", "137438691328", "549754765312", "2199022206976", "8796095119360", "35184380477440", "140737496743936", "562949936644096" ]
[ "nonn", "easy" ]
7
0
4
[ "A007582", "A047849", "A071930", "A377840", "A377883", "A377885", "C2", "C8", "D4", "D8", "M4", "Q8" ]
null
Sean A. Irvine, Nov 10 2024
2024-11-12T12:17:47
oeisdata/seq/A377/A377885.seq
0aa15d82205b5f45971923c64a0accb0
A377886
Prime-based Brazilian numbers: numbers k such that there is a prime number p with 1 < p < k-1 such that the representation of k in base p has all equal digits.
[ "7", "8", "12", "13", "15", "16", "18", "24", "26", "28", "31", "32", "36", "40", "42", "48", "54", "56", "57", "60", "62", "63", "64", "70", "72", "76", "80", "84", "88", "90", "93", "96", "98", "100", "108", "112", "114", "120", "121", "124", "126", "127", "128", "132", "133", "136", "140", "144", "148", "150", "152", "154", "156", "160", "162", "168", "171", "176", "180", "183", "186", "190", "192", "196", "198", "200", "204", "208", "210", "216", "220", "222", "224", "228", "234", "240", "242", "248", "252" ]
[ "nonn" ]
33
1
1
[ "A125134", "A377886" ]
null
Frank M Jackson, Nov 12 2024
2024-11-13T16:32:51
oeisdata/seq/A377/A377886.seq
26d80252d9be918f36ec1bc51c41a95c
A377887
a(n) is the number of ways of writing prime(n) as k-q with q a prime and k a primorial.
[ "0", "1", "0", "1", "2", "3", "4", "3", "3", "3", "1", "3", "4", "4", "5", "4", "5", "3", "4", "4", "5", "4", "4", "7", "8", "6", "5", "7", "4", "5", "9", "5", "6", "5", "9", "7", "4", "5", "8", "5", "8", "6", "7", "5", "9", "6", "5", "7", "6", "4", "3", "9", "6", "5", "12", "8", "5", "6", "7", "7", "6", "9", "8", "7", "13", "4", "8", "4", "6", "6", "7", "4", "7", "11", "5", "8", "8", "9", "6", "7", "7", "6", "12", "4", "10", "11", "11", "7", "8", "11" ]
[ "nonn" ]
20
1
5
[ "A002110", "A175933", "A377887" ]
null
Daniel D Gibson, Nov 10 2024
2024-12-12T23:33:07
oeisdata/seq/A377/A377887.seq
3a70ea7306e2623275b629e97946f04f
A377888
E.g.f. A(x) satisfies A(x) = exp(x * A(x))/(1 - x*A(x)^2).
[ "1", "2", "17", "289", "7541", "267041", "11974645", "650666731", "41560476809", "3052145052433", "253400719220801", "23470964805942083", "2399562226994185885", "268404500411311273465", "32606551238103342068717", "4275233840499570086190331", "601753408713140793660643985", "90500525005651471292191270433" ]
[ "nonn" ]
9
0
2
[ "A352410", "A371318", "A377831", "A377888", "A377889" ]
null
Seiichi Manyama, Nov 10 2024
2024-11-11T06:45:56
oeisdata/seq/A377/A377888.seq
f3915421cae2529d00e4264937f59742
A377889
E.g.f. A(x) satisfies A(x) = exp(x * A(x))/(1 - x*A(x)^3).
[ "1", "2", "21", "472", "16581", "795736", "48509641", "3589729760", "312603962985", "31321633489408", "3549706188092541", "448973808123051520", "62697159481460439469", "9581292408000225087488", "1590488540940006100524657", "284993765391981838318575616", "54826610288277007690469896017" ]
[ "nonn" ]
9
0
2
[ "A352410", "A373324", "A377831", "A377888", "A377889" ]
null
Seiichi Manyama, Nov 10 2024
2024-11-11T06:47:01
oeisdata/seq/A377/A377889.seq
037cc8aca03bef4d054c3d7ed0cda703
A377890
E.g.f. A(x) satisfies A(x) = (1 + x*A(x)^2) * exp(x * A(x)).
[ "1", "2", "15", "211", "4433", "124741", "4412815", "188335981", "9421966209", "540884623753", "35054089163351", "2531882857204273", "201689970517618225", "17567711167993834381", "1661084543502646535967", "169448367505003640681221", "18550123929621138841581185", "2169272360350263071212545553" ]
[ "nonn" ]
11
0
2
[ "A088690", "A377826", "A377890", "A377891" ]
null
Seiichi Manyama, Nov 11 2024
2024-12-29T08:48:54
oeisdata/seq/A377/A377890.seq
9ea9a47a9f04a392a50a77ea63c69cae
A377891
E.g.f. A(x) satisfies A(x) = (1 + x*A(x)^3) * exp(x * A(x)).
[ "1", "2", "19", "364", "10665", "423056", "21221851", "1288931456", "91977076561", "7543664425216", "699290913249891", "72306463481715200", "8251192866018497401", "1030074741274860240896", "139650729116792108398891", "20432888021354725476499456", "3209204194084043665909835937", "538542735919965101952197525504" ]
[ "nonn" ]
9
0
2
[ "A088690", "A377826", "A377890", "A377891" ]
null
Seiichi Manyama, Nov 11 2024
2024-11-11T06:49:01
oeisdata/seq/A377/A377891.seq
61c45bb53320fc42a21285324e5cc8f8
A377892
E.g.f. A(x) satisfies A(x) = (1 + x*A(x)^2) * exp(x * A(x)^2).
[ "1", "2", "19", "352", "9885", "374486", "17907991", "1035748260", "70334590969", "5487022612810", "483655093883451", "47541690024105608", "5156503816883562325", "611769291578643110238", "78812382009451814165695", "10956572374811382997014796", "1634950184384280878142249969", "260653481562714033459279871250" ]
[ "nonn" ]
8
0
2
[ "A088690", "A377892", "A377893" ]
null
Seiichi Manyama, Nov 11 2024
2024-11-11T06:50:31
oeisdata/seq/A377/A377892.seq
9379e3f2b8ffa6e6ceb8017fe3adac10
A377893
E.g.f. A(x) satisfies A(x) = (1 + x*A(x)^3) * exp(x * A(x)^3).
[ "1", "2", "27", "742", "31337", "1796376", "130408603", "11472417104", "1186462228785", "141083381264896", "18966727953873371", "2844742575536036352", "470958524169176911513", "85307709328403287961600", "16782586179544965856158363", "3563492814539574559964993536", "812273035493592514001487147233" ]
[ "nonn" ]
8
0
2
[ "A088690", "A377892", "A377893" ]
null
Seiichi Manyama, Nov 11 2024
2024-11-11T06:51:29
oeisdata/seq/A377/A377893.seq
6e22a1b02bbee138fb662a659860e258
A377894
E.g.f. satisfies A(x) = (1 + x) * exp(x * A(x)^2).
[ "1", "2", "11", "142", "2725", "71026", "2339719", "93311758", "4371948137", "235418287042", "14327098759171", "972533690209390", "72854996624174989", "5970582808814848498", "531359818098465084863", "51034785131352404960686", "5261620527219949295345233", "579593410301187097865649922" ]
[ "nonn" ]
10
0
2
[ "A377826", "A377894", "A377895" ]
null
Seiichi Manyama, Nov 11 2024
2025-02-16T08:34:07
oeisdata/seq/A377/A377894.seq
3ef5bda65088922b1b9750a7dcb957a5
A377895
E.g.f. satisfies A(x) = (1 + x) * exp(x * A(x)^3).
[ "1", "2", "15", "283", "8057", "313161", "15436735", "922964771", "64910124753", "5250807814753", "480339263735831", "49032749858906067", "5525542086267361801", "681359718334607629409", "91259859216031641999375", "13193464971338727171704611", "2047721360761921797402720545", "339610337568547449759788735553" ]
[ "nonn" ]
8
0
2
[ "A377826", "A377894", "A377895" ]
null
Seiichi Manyama, Nov 11 2024
2025-02-16T08:34:07
oeisdata/seq/A377/A377895.seq
3c0eb73f4fb9d8cc59cdcf65d457d6ca
A377896
a(n) is the number of occurrences of n in A377862.
[ "1", "2", "2", "3", "3", "4", "4", "4", "5", "5", "5", "6", "6", "6", "6", "7", "7", "7", "7", "8", "8", "8", "8", "9", "9", "9", "9", "9", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "3", "1", "3", "1", "3", "1", "3", "1", "3", "1", "3", "1", "4", "1", "4", "1", "4", "1", "4", "1", "4", "1", "4", "1", "5", "1" ]
[ "nonn", "base" ]
6
1
2
[ "A377862", "A377863", "A377896" ]
null
Rémy Sigrist, Nov 11 2024
2024-11-11T12:03:52
oeisdata/seq/A377/A377896.seq
8f6ed6efe83dc769b7062c7639276071
A377897
Numbers k such that k + PrimePi(k) is even.
[ "4", "5", "8", "10", "11", "14", "16", "17", "20", "22", "23", "25", "27", "30", "31", "33", "35", "38", "40", "41", "44", "46", "47", "49", "51", "54", "56", "58", "59", "62", "64", "66", "67", "69", "72", "73", "75", "77", "80", "82", "83", "85", "87", "90", "92", "94", "96", "97", "99", "102", "103", "105", "108", "109", "111", "114", "116", "118", "120", "122", "124", "126", "127", "129", "132", "134", "136", "137", "140" ]
[ "nonn" ]
20
1
1
[ "A000720", "A121053", "A377897", "A377994" ]
null
N. J. A. Sloane, Nov 13 2024
2024-11-14T05:31:41
oeisdata/seq/A377/A377897.seq
804a898437e56d8d93495c0baa1bafd9
A377898
A121053 sorted into increasing order, or, equivalently, the indices of prime terms in A121053.
[ "1", "2", "3", "5", "7", "8", "10", "11", "13", "14", "16", "17", "19", "20", "22", "23", "25", "27", "29", "30", "31", "33", "35", "37", "38", "40", "41", "43", "44", "46", "47", "49", "51", "53", "54", "56", "58", "59", "61", "62", "64", "66", "67", "69", "71", "72", "73", "75", "77", "79", "80", "82", "83", "85", "87", "89", "90", "92", "94", "96", "97", "99", "101", "102", "103", "105", "107", "108", "109", "111", "113", "114", "116", "118", "120", "122", "124", "126", "127", "129", "131", "132", "134", "136", "137", "139" ]
[ "nonn" ]
6
1
2
[ "A099862", "A121053", "A377898" ]
null
N. J. A. Sloane, Nov 14 2024
2024-11-15T22:39:11
oeisdata/seq/A377/A377898.seq
10299c99ca87ebcaa747b1eb83395080
A377899
a(n) = number of composite numbers c_{2*k+1} <= n, where c_m = A002808(m) is the m-th composite number.
[ "0", "0", "0", "1", "1", "1", "1", "2", "2", "3", "3", "3", "3", "4", "4", "5", "5", "5", "5", "6", "6", "7", "7", "7", "8", "8", "9", "9", "9", "10", "10", "10", "11", "11", "12", "12", "12", "13", "13", "14", "14", "14", "14", "15", "15", "16", "16", "16", "17", "17", "18", "18", "18", "19", "19", "20", "20", "21", "21", "21", "21", "22", "22", "23", "23", "24", "24", "24", "25", "25", "25", "26", "26", "26", "27", "27", "28", "28", "28", "29", "29", "30", "30", "30", "31", "31", "32", "32", "32", "33", "33", "34", "34", "35", "35", "36", "36", "36", "37", "37", "37" ]
[ "nonn" ]
11
1
8
[ "A000720", "A002808", "A062298", "A099861", "A377899" ]
null
N. J. A. Sloane, Nov 14 2024
2024-11-15T09:03:43
oeisdata/seq/A377/A377899.seq
7bfe5a62e5cd735a1fcd308283e446b3
A377900
After A121053(n) has been found, a(n) is the smallest candidate for A121053(n+1) that has not been eliminated.
[ "1", "1", "1", "6", "6", "9", "9", "9", "12", "12", "12", "15", "15", "15", "18", "18", "18", "21", "21", "21", "24", "24", "24", "26", "26", "28", "28", "32", "32", "32", "32", "34", "34", "36", "36", "39", "39", "39", "42", "42", "42", "45", "45", "45", "48", "48", "48", "50", "50", "52", "52", "55", "55", "55", "57", "57", "60", "60", "60", "63", "63", "63", "65", "65", "68", "68", "68", "70" ]
[ "nonn" ]
9
1
4
[ "A099862", "A121053", "A377898", "A377900" ]
null
N. J. A. Sloane, Nov 14 2024
2024-11-29T07:36:25
oeisdata/seq/A377/A377900.seq
a3b83657b397a3ae4b7dcf1fe441ff77
A377901
Let Q consist of 1 together with the primes (A008578); form the lexicographically earliest infinite sequence S of distinct positive numbers with the property that a(k) is in Q if and only if k is a term in S.
[ "1", "2", "3", "5", "7", "4", "11", "9", "13", "12", "17", "19", "23", "15", "29", "18", "31", "37", "41", "21", "43", "24", "47", "53", "26", "59", "28", "61", "67", "32", "71", "73", "34", "79", "36", "83", "89", "39", "97", "42", "101", "103", "107", "45", "109", "48", "113", "127", "50", "131", "52", "137", "139", "55", "149", "57", "151", "60", "157", "163", "167", "63", "173", "65" ]
[ "nonn" ]
24
1
2
[ "A008578", "A121053", "A377901", "A379051", "A379053" ]
null
N. J. A. Sloane, Nov 15 2024
2024-12-18T09:21:23
oeisdata/seq/A377/A377901.seq
ad3d69a9e3888ad563a65fd8d7d1f03a
A377902
First differences of A377898.
[ "1", "1", "2", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "2", "2", "1", "1", "2", "2", "2", "1", "2", "1", "2", "1", "2", "1", "2", "2", "2", "1", "2", "2", "1", "2", "1", "2", "2", "1", "2", "2", "1", "1", "2", "2", "2", "1", "2", "1", "2", "2", "2", "1", "2", "2", "2", "1", "2", "2", "1", "1", "2", "2", "1", "1", "2", "2", "1", "2", "2", "2", "2", "2", "2", "1", "2", "2", "1", "2", "2", "1", "2", "1", "2", "2", "2", "2", "1", "2", "1", "2", "2", "1", "2", "2", "2", "1", "2", "1", "2", "2", "2", "1", "2", "2", "1", "2", "1", "2", "2", "2", "2", "1", "2", "1", "2", "1", "2", "1", "2", "2", "2", "2" ]
[ "nonn" ]
3
1
3
[ "A121053", "A377898", "A377902" ]
null
N. J. A. Sloane, Nov 15 2024
2024-11-15T13:04:31
oeisdata/seq/A377/A377902.seq
d47d02df2c6684112760985a6398e630
A377903
Indices of records in A302656.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "20", "97", "176", "396", "463", "1918", "1984", "2278" ]
[ "nonn", "more" ]
24
1
2
[ "A302656", "A376769", "A376776", "A377903", "A377904", "A377906", "A377911" ]
null
N. J. A. Sloane, Nov 19 2024
2024-11-24T09:20:51
oeisdata/seq/A377/A377903.seq
11a586c5a35af84e37dae98713495bad