A056006 Numbers k such that k | sigma(k) + 2.

1, 3, 10, 136, 32896, 2147516416

Offset: 1

Author

Robert G. Wilson v, Jul 24 2000

Keywords

• nonn
• more

Comments

n | sigma(n) gives the multi-perfect numbers A007691, n | sigma(n)+1 if n is a power of 2 (A000079).

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

a(7) > 10^13. - Giovanni Resta, Jul 13 2015

a(7) > 10^18. - Max Alekseyev, May 27 2025

Crossrefs

Cf. A000203, A045768, A055708.

Programs

Mathematica

Do[If[Mod[DivisorSigma[1, n]+2, n]==0, Print[n]], {n, 1, 7*10^8}]

PARI

for(n=1,5e9,if((sigma(n)+2)%n==0,print1(n", "))) \\ Charles R Greathouse IV, Jun 01 2011

Extensions

a(6) from Charles R Greathouse IV, Jun 01 2011

Edited by M. F. Hasler, Oct 02 2014