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%I #16 Oct 20 2021 11:55:06
%S 0,5,28,1060,3126,233885,823544,201351372,2324524398,70000350147,
%T 285311670612,142657631177872,302875106592254,100008061904383173,
%U 3503151123048905408,590295810427425653792,827240261886336764178,826274569583310299739525,1978419655660313589123980,2516582400000122880019968984
%N a(n) = Sum_{d|n} (n^d)', where ' is the arithmetic derivative.
%F If p is prime, a(p) = p^p + 1. See A125137. - _Bernard Schott_, Oct 18 2021
%e a(4) = 1060; a(4) = (4^1)' + (4^2)' + (4^4)' = 4' + 16' + 256' = 4 + 32 + 1024 = 1060.
%t d[0] = d[1] = 0; d[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); a[n_] := DivisorSum[n, d[n^#] &]; Array[a, 20] (* _Amiram Eldar_, Oct 16 2021 *)
%o (PARI) ad(n) = vecsum([n/f[1]*f[2]|f<-factor(n+!n)~]); \\ A003415
%o a(n) = sumdiv(n, d, ad(n^d)); \\ _Michel Marcus_, Oct 18 2021
%Y Cf. A003415, A125137.
%K nonn
%O 1,2
%A _Wesley Ivan Hurt_, Oct 16 2021
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