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a(n) = Sum_{p|n, p prime} n^prime(n/p).
1

%I #6 Jun 26 2024 15:15:16

%S 0,4,9,64,25,7992,49,2097152,59049,100000001000,121,106993241210880,

%T 169,30491346729331198648,8649756618750,75557863725914323419136,289,

%U 74347713614042750878184448000,361,53687091200000000000000000001280000000,30041942495081695978842,412195366437884247746798137865015318817176

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

%F a(p^k) = p^(k*prime(p^(k-1))), for p prime and k >= 1. - _Wesley Ivan Hurt_, Jun 26 2024

%t Table[DivisorSum[n, n^Prime[n/#] &, PrimeQ[#] &], {n, 30}]

%Y Cf. A000040, A351368, A369748.

%K nonn,easy

%O 1,2

%A _Wesley Ivan Hurt_, Feb 03 2024