A049603 (1+e)-sigma perfect numbers: (1+e) - sigma(x) = 2*x.

6, 28, 264, 1104, 3360, 75840, 6499584, 151062912, 2171581440, 4686409728, 316023611904

Offset: 1

Author

Yasutoshi Kohmoto

Keywords

• nonn
• nice

Comments

The function (1+e) - sigma(n) is defined in A051378. This sequence lists solutions to A051378(n) = 2*n.

a(12) > 10^12. - Giovanni Resta, Jun 12 2016

Examples

			Factorizations: 2*3, 2^2*7, 2^3*3*11, 2^4*3*23, 2^5*3*5*7, 2^6*3*5*79, 2^8*3^2*7*13*31, 2^7*3^2*7*11*13*131, 2^10*3*5*7*19*1063.
		

Crossrefs

Cf. A049599, A051378.

Programs

Mathematica

(* Assuming all terms greater than 28 are multiple of 24 *) ok[n_] := 2*n == Times @@ (1 + Sum[First[#]^s, {s, Divisors[Last[#]]}] & ) /@ FactorInteger[n]; Reap[For[n = 2, n <= 2171581440, n = n + If[n < 48, 1, 24], If[ok[n], Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Jun 26 2012 *)

Extensions

151062912 inserted by Jean-François Alcover, Jun 26 2012

a(10)-a(11) from Giovanni Resta, Jun 12 2016