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%I #6 Jul 09 2025 16:34:24
%S 0,1,1,16,1,252,1,64,729,100100,1,248976,1,105413700,762750,256,1,
%T 1895400,1,1280000400,1801097802,584318301411812,1,7963200,9765625,
%U 2481152873203737252,19683,10578455954192,1,677994300000,1,1024,50542106513762754
%N a(n) = Sum_{p|n, p prime} n^sopf(n/p).
%F a(p^k) = p^(p*(k-floor(1/k))) for p prime and k>=1. - _Wesley Ivan Hurt_, Jul 09 2025
%t a[n_] := Sum[p, {p, Select[Divisors[n], PrimeQ]}]; Table[DivisorSum[n, n^a[n/#] &, PrimeQ[#] &], {n, 40}]
%Y Cf. A008472 (sopf), A369744, A369911, A369912.
%K nonn,easy
%O 1,4
%A _Wesley Ivan Hurt_, Feb 05 2024