A369912 -id:A369912

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A369913

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

+10
1

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

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OFFSET

1,4

LINKS

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

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.

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Feb 05 2024

STATUS

approved

A369914

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

+10
0

0, 0, 0, 4, 0, 13, 0, 8, 9, 29, 0, 38, 0, 53, 34, 16, 0, 57, 0, 78, 58, 125, 0, 76, 25, 173, 27, 134, 0, 220, 0, 32, 130, 293, 74, 150, 0, 365, 178, 156, 0, 366, 0, 294, 147, 533, 0, 152, 49, 195, 298, 398, 0, 171, 146, 268, 370, 845, 0, 500, 0, 965, 237, 64, 194