A394725 Numbers k such that the sum of its proper divisors, each to some power greater than zero, is equal to 2*k.

6, 12, 20, 22, 24, 40, 42, 48, 54, 56, 60, 66, 78, 86, 90, 96, 108, 116, 120, 126, 132, 136, 138, 140, 150, 160, 168, 174, 190, 192, 198, 204, 210, 212, 216, 220, 222, 224, 234, 246, 258, 264, 270, 272, 276, 280, 282, 294, 300, 306, 308, 312, 320, 330, 342, 348, 350

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..57.

Example

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.

Mathematica

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 *)

Crossrefs

Sequence in context: A235268 A354931 A105455 * A345919 A246198 A083207

Adjacent sequences: A394722 A394723 A394724 * A394726 A394727 A394728

Keyword

nonn

Author

Leo Hennig, Mar 30 2026

Extensions

More terms from Amiram Eldar, Mar 30 2026

Status

approved