A247111 - OEIS

A247111

Integers such that sigma(sigma(n) - n) = 2*n, where sigma is the sum of divisors, A000203.

6, 28, 36, 496, 8128, 33550336, 8589869056

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OFFSET

1,1

COMMENTS

That is, integers such that A072869(n) = 2*n.

All perfect numbers (A000396) belong to this sequence.

Is there another term like 36 that is not perfect?

a(8) > 10^11. - Hiroaki Yamanouchi, Sep 11 2015

a(8) <= 137438691328. - David A. Corneth, Jun 04 2021

LINKS

EXAMPLE

For n=36, sigma(sigma(36)-36) = sigma(91-36) = sigma(55) = 72, hence 36 is in the sequence.

MATHEMATICA

Select[Range[1, 10000], DivisorSigma[1, DivisorSigma[1, #]-#]==2*#&] (* Julien Kluge, Sep 20 2016 *)

PROG

(PARI) isok(n) = (sigma(sigma(n) - n) == 2*n);

CROSSREFS

Cf. A000203 (sigma(n)), A000396 (perfect numbers), A001065 (sigma(n)-n), A072869 (sigma(sigma(n)-n).

KEYWORD

nonn,more

AUTHOR

EXTENSIONS

a(7) from Michel Marcus, Nov 22 2014

STATUS

approved