A247111 - OEIS

%I #36 Nov 15 2024 03:05:43

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

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

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

%C All perfect numbers (A000396) belong to this sequence.

%C Is there another term like 36 that is not perfect?

%C a(8) > 10^11. - _Hiroaki Yamanouchi_, Sep 11 2015

%C a(8) <= 137438691328. - _David A. Corneth_, Jun 04 2021

%H <a href="/index/O#opnseqs">Index entries for sequences where odd perfect numbers must occur, if they exist at all</a>

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

%t Select[Range[1,10000],DivisorSigma[1,DivisorSigma[1,#]-#]==2*#&] (* _Julien Kluge_, Sep 20 2016 *)

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

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

%Y Cf. also A019283, A326181, A342922.

%K nonn,more

%O 1,1

%A _Michel Marcus_, Nov 19 2014

%E a(7) from _Michel Marcus_, Nov 22 2014