A348278 a(n) = Sum_{d|n} d^(d').

1, 3, 4, 259, 6, 7782, 8, 68719476995, 531445, 10000008, 12, 184884258895044454, 14, 20661046794, 2562890634, 340282366920938463463374607500487688451, 18, 229468251895129407140411991, 20, 16777216000000000000000010000264, 16679880978212

Offset

1,2

Links

Table of n, a(n) for n=1..21.

Formula

a(p) = p + 1 for primes p since we have 1^(1') + p^(p') = 1^0 + p^1 = p + 1.

Example

a(4) = 259; a(4) = 1^(1') + 2^(2') + 4^(4') = 1^0 + 2^1 + 4^4 = 1 + 2 + 256 = 259.

Prog

(PARI) ad(n) = vecsum([n/f[1]*f[2]|f<-factor(n+!n)~]); \\ A003415
a(n) = sumdiv(n, d, d^ad(d)); \\ Michel Marcus, Oct 10 2021

Crossrefs

Cf. A003415 (arithmetic derivative).

Sequence in context: A111315 A042711 A195566 * A348280 A304150 A305505

Adjacent sequences: A348275 A348276 A348277 * A348279 A348280 A348281

Keyword

nonn

Author

Wesley Ivan Hurt, Oct 09 2021

Status

approved