A394725 - OEIS

%I #22 Apr 18 2026 20:07:33

%S 6,12,20,22,24,40,42,48,54,56,60,66,78,86,90,96,108,116,120,126,132,

%T 136,138,140,150,160,168,174,190,192,198,204,210,212,216,220,222,224,

%U 234,246,258,264,270,272,276,280,282,294,300,306,308,312,320,330,342,348,350

%N Numbers k such that the sum of its proper divisors, each to some power greater than zero, is equal to 2*k.

%C Is this equal to the numbers that have such an exponent configuration for k^2 instead of 2*k? Looks like the terms for k^2 are a subsequence.

%e For 48, exponents: 1, 2, 2, 2, 1, 1, 1, 1, 1, divisors: 1, 2, 3, 4, 6, 8, 12, 16, 24 and 2 * 48 = 96 is equal to: 1 + 2^2 + 3^2 + 4^2 + 6 + 8 + 12 + 16 + 24. So 48 is a term.

%t q[k_] := Module[{d = Most[Divisors[k]], e}, e = Join[{1}, Floor[Log[Rest[d], 2*k]]]; AnyTrue[Tuples[Range /@ e], Total[d^#] == 2*k &]]; Select[Range[2, 350], q] (* _Amiram Eldar_, Mar 30 2026 *)

%K nonn

%O 1,1

%A _Leo Hennig_, Mar 30 2026

%E More terms from _Amiram Eldar_, Mar 30 2026