A369913 a(n) = Sum_{p|n, p prime} n^sopf(n/p).

0, 1, 1, 16, 1, 252, 1, 64, 729, 100100, 1, 248976, 1, 105413700, 762750, 256, 1, 1895400, 1, 1280000400, 1801097802, 584318301411812, 1, 7963200, 9765625, 2481152873203737252, 19683, 10578455954192, 1, 677994300000, 1, 1024, 50542106513762754

Offset

1,4

Links

Table of n, a(n) for n=1..33.

Formula

a(p^k) = p^(p*(k-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, n^a[n/#] &, PrimeQ[#] &], {n, 40}]

Crossrefs

Cf. A008472 (sopf), A369744, A369911, A369912.

Sequence in context: A351244 A105671 A145828 * A371081 A223518 A095876

Adjacent sequences: A369910 A369911 A369912 * A369914 A369915 A369916

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Feb 05 2024

Status

approved