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A232354 Numbers n such that n divides sigma(n^2). 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Sigma(n) = A000203(n) = sum of divisors of n.

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

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

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Last modified June 1 19:32 EDT 2020. Contains 334762 sequences. (Running on oeis4.)