A052396 (+2)-sigma perfect numbers: numbers k such that (+2)sigma(k) = 2*k, where (+2)sigma(k) = A107758(k).

2, 4, 8, 16, 32, 63, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 34587, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 170271801, 268435456, 536870912, 1073741824, 2147483648, 4294967296

Offset: 1

Author

Yasutoshi Kohmoto Mar 13 2000

Keywords

• nonn

Comments

2^n is a term for all n>=1. - Amiram Eldar, Aug 26 2022

Examples

			Factorizations: even examples: 2, 2^2, 2^3, 2^4,...; odd examples: a(6) = 3^2*7, a(17) = 3^4*7*61, a(30) = 3^6*7*61*547.
		

Crossrefs

Cf. A000079, A107758.

Programs

Mathematica

f[p_, e_] := 1 + (p^(e + 1) - 1)/(p - 1); s[n_] := Times @@ f @@@ FactorInteger[n]; s[1] = 1; Select[Range[5*10^6], s[#] == 2*# &] (* Amiram Eldar, Aug 26 2022 *)

Extensions

Corrected by Franklin T. Adams-Watters, Oct 25 2006

a(30) corrected and a(31)-a(35) added by Amiram Eldar, Aug 26 2022