A247111 Integers k such that sigma(sigma(k) - k) = 2*k, where sigma is the sum of divisors, A000203.

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

Offset: 1

Author

Michel Marcus, Nov 19 2014

Keywords

• nonn
• more

Comments

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

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

Examples

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

Links

• Index entries for sequences where odd perfect numbers must occur, if they exist at all

Crossrefs

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

Cf. also A019283, A326181, A342922.

Programs

Mathematica

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

PARI

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

Extensions

a(7) from Michel Marcus, Nov 22 2014