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%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