A369912 a(n) = Sum_{p|n, p prime} p^sopf(n/p).

0, 1, 1, 4, 1, 17, 1, 4, 27, 57, 1, 41, 1, 177, 368, 4, 1, 251, 1, 153, 2530, 2169, 1, 41, 3125, 8361, 27, 561, 1, 5568, 1, 4, 178478, 131361, 94932, 275, 1, 524649, 1596520, 153, 1, 37514, 1, 8313, 6686, 8389137, 1, 41, 823543, 78157, 129145076, 32937, 1, 251

Offset

1,4

Links

Table of n, a(n) for n=1..54.

Formula

a(p^k) = p^(p-p*floor(1/k)) for p prime and k>=1. - Wesley Ivan Hurt, Jul 09 2025

Mathematica

a[n_] := Sum[p, {p, Select[Divisors[n], PrimeQ]}]; Table[DivisorSum[n, #^a[n/#] &, PrimeQ[#] &], {n, 80}]

Crossrefs

Cf. A008472 (sopf), A369744, A369911, A369913.

Sequence in context: A072651 A380570 A209411 * A093035 A301624 A126791

Adjacent sequences: A369909 A369910 A369911 * A369913 A369914 A369915

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Feb 05 2024

Status

approved