A232354 Numbers k that divide sigma(k^2) where sigma is the sum of divisors function (A000203).

1, 39, 793, 2379, 7137, 13167, 76921, 78507, 230763, 238887, 549549, 692289, 863577, 1491633, 1672209, 2076867, 4317885, 7615179, 8329831, 10441431, 23402223, 24989493, 37776123, 53306253, 53695813, 55871145, 74968479, 83766969, 133854435, 144688401, 161087439, 189437391

Offset

1,2

Comments

Squarefree terms are: 1, 39, 793, 2379, 76921, 230763, 8329831, 24989493, 53695813, 161087439, ... Quotients are: 1, 61, 873, 3783, 11737, 26543, 85563, 141911, 370773, 417263, 1155561, ... - Michel Marcus, Nov 23 2013

Many terms are also in sequence A069520, cf. A232067 for the intersection of these two sequences. - M. F. Hasler, Nov 24 2013

Links

Donovan Johnson, Table of n, a(n) for n = 1..200

Jose Arnaldo Bebita Dris, A new approach to odd perfect numbers via GCDs, arXiv:2202.08116 [math.NT], 2022.

Formula

A065764(a(n)) mod a(n) = 0.

Mathematica

Select[Range[10^5], Divisible[DivisorSigma[1, #^2], #] &] (* Alonso del Arte, Dec 06 2013 *)

Prog

(PARI) isok(n) = (sigma(n^2) % n) == 0; \\ Michel Marcus, Nov 23 2013

Crossrefs

Cf. A000203, A007691, A065764, A069520, A227302, A232067, A232703, A232704.

Sequence in context: A221358 A194133 A069520 * A232067 A247222 A268983

Adjacent sequences: A232351 A232352 A232353 * A232355 A232356 A232357

Keyword

nonn

Author

Alex Ratushnyak, Nov 22 2013

Status

approved