cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A227306 Numbers k that divide sigma(k) + sigma(k-1).

Original entry on oeis.org

2, 6, 34, 50, 216, 236, 262, 386, 898, 924, 945, 1456, 2380, 5356, 6468, 6624, 8362, 14100, 23496, 26938, 46594, 80876, 196344, 212796, 1661136, 4070200, 4160920, 4626700, 5244548, 5462384, 17062316, 60464628, 217408416, 248621604, 262792908, 265371336, 323987588
Offset: 1

Views

Author

Alex Ratushnyak, Jul 05 2013

Keywords

Comments

Is 945 the only odd term? - Zak Seidov, Jul 06 2013
945 and 19910536425 are the only odd terms below 2^36. - Alex Ratushnyak, Jul 08 2013
The third odd term is a(58) = 841488503841. - Giovanni Resta, Apr 04 2014

Crossrefs

Programs

  • Mathematica
    With[{nn=324*10^6},Select[Thread[{Total/@Partition[DivisorSigma[ 1,Range[ nn]],2,1],Range[ 2,nn]}],Divisible[#[[1]],#[[2]]]&][[All,2]]] (* Harvey P. Dale, May 29 2020 *)

A346140 Numbers m such that there exist positive integers i <= m and j >= m such that m = Sum_{k=i..j} A001065(k), where A001065(k) = sum of the proper divisors of k, and i and j do not both equal m.

Original entry on oeis.org

2, 4, 5, 7, 8, 16, 29, 32, 39, 121, 128, 256, 279, 469, 1299, 3477, 7299, 7525, 8192, 13969, 19262, 19909, 26739, 31493, 54722, 65536, 99381, 131072, 357699, 524288, 13204262, 20742483, 33550337, 72873362
Offset: 1

Views

Author

Scott R. Shannon, Jul 05 2021

Keywords

Comments

No perfect numbers are included as it is required i and j cannot both equal m. Any prime number that is one more than a perfect number will appear in the sequence.

Examples

			2 is a term as A001065(2) = 1, A001065(3) = 1, and 1 + 1 = 2.
5 is a term as A001065(3) = 1, A001065(4) = 3, A001065(5) = 1, and 1 + 3 + 1 = 5.
29 is a term as A001065(28) = 28, A001065(29) = 1, and 28 + 1 = 29. This is an example of a prime number one more than a perfect number, thus it will appear in the sequence.
121 is a term as A001065(121) = 12, A001065(122) = 64, A001065(123) = 45, and 12 + 64 + 45 = 121.
19262 is a term as A001065(19261) = 3203, A001065(19262) = 9634, A001065(19263) = 6425, and 3203 + 9634 + 6425 = 19262. This is the first term that requires i < m and j > m.
		

Crossrefs

Showing 1-2 of 2 results.