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%I #14 Jul 13 2015 05:15:32
%S 1,3,10,136,32896,2147516416
%N Numbers n such that n | sigma(n) + 2.
%C n | sigma(n) gives the multi-perfect numbers A007691, n | sigma(n)+1 if n is a power of 2 (A000079).
%C 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 a(7) > 10^13. - _Giovanni Resta_, Jul 13 2015
%t Do[If[Mod[DivisorSigma[1, n]+2, n]==0, Print[n]], {n, 1, 7*10^8}]
%o (PARI) for(n=1,5e9,if((sigma(n)+2)%n==0,print1(n", "))) \\ _Charles R Greathouse IV_, Jun 01 2011
%Y Cf. A000203, A045768, A055708.
%K nonn,more
%O 1,2
%A _Robert G. Wilson v_, Jul 24 2000
%E a(6) from _Charles R Greathouse IV_, Jun 01 2011
%E Edited by _M. F. Hasler_, Oct 02 2014