A348393 a(n) = Sum_{d|n} (n^d)', where ' is the arithmetic derivative.

0, 5, 28, 1060, 3126, 233885, 823544, 201351372, 2324524398, 70000350147, 285311670612, 142657631177872, 302875106592254, 100008061904383173, 3503151123048905408, 590295810427425653792, 827240261886336764178, 826274569583310299739525, 1978419655660313589123980, 2516582400000122880019968984

Offset

1,2

Links

Table of n, a(n) for n=1..20.

Formula

If p is prime, a(p) = p^p + 1. See A125137. - Bernard Schott, Oct 18 2021

Example

a(4) = 1060; a(4) = (4^1)' + (4^2)' + (4^4)' = 4' + 16' + 256' = 4 + 32 + 1024 = 1060.

Mathematica

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 *)

Prog

(PARI) ad(n) = vecsum([n/f[1]*f[2]|f<-factor(n+!n)~]); \\ A003415
a(n) = sumdiv(n, d, ad(n^d)); \\ Michel Marcus, Oct 18 2021

Crossrefs

Cf. A003415, A125137.

Sequence in context: A346312 A359739 A344464 * A057642 A125137 A348350

Adjacent sequences: A348390 A348391 A348392 * A348394 A348395 A348396

Keyword

nonn

Author

Wesley Ivan Hurt, Oct 16 2021

Status

approved