This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A056006 #21 Jun 11 2025 12:33:08
%S A056006 1,3,10,136,32896,2147516416
%N A056006 Numbers k such that k | sigma(k) + 2.
%C A056006 n | sigma(n) gives the multi-perfect numbers A007691, n | sigma(n)+1 if n is a power of 2 (A000079).
%C A056006 This contains A191363 as subsequence, so for any Fermat prime F(k) = 2^2^k+1, the triangular number A000217(2^2^k)=(F(k)-1)*F(k)/2 is in this sequence. See also A055708 which is identical up to the first term. - _M. F. Hasler_, Oct 02 2014
%C A056006 a(7) > 10^13. - _Giovanni Resta_, Jul 13 2015
%C A056006 a(7) > 10^18. - _Max Alekseyev_, May 27 2025
%t A056006 Do[If[Mod[DivisorSigma[1, n]+2, n]==0, Print[n]], {n, 1, 7*10^8}]
%o A056006 (PARI) for(n=1,5e9,if((sigma(n)+2)%n==0,print1(n", "))) \\ _Charles R Greathouse IV_, Jun 01 2011
%Y A056006 Cf. A000203, A045768, A055708.
%K A056006 nonn,more
%O A056006 1,2
%A A056006 _Robert G. Wilson v_, Jul 24 2000
%E A056006 a(6) from _Charles R Greathouse IV_, Jun 01 2011
%E A056006 Edited by _M. F. Hasler_, Oct 02 2014