A348280 a(n) = Sum_{d|n} n^(d').

1, 3, 4, 261, 6, 7789, 8, 68719480841, 531451, 10000021, 12, 184884258895306009, 14, 20661046813, 2562890656, 340282366920938463463374888906744987665, 18, 229468251895129407175774597, 20, 16777216000000000000001280160041, 16679880978244

Offset

1,2

Links

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

Formula

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

Example

a(4) = 261; a(4) = 4^(1') + 4^(2') + 4^(4') = 4^0 + 4^1 + 4^4 = 1 + 4 + 256 = 261.

Prog

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

Crossrefs

Cf. A003415 (arithmetic derivative).

Sequence in context: A042711 A195566 A348278 * A304150 A305505 A069970

Adjacent sequences: A348277 A348278 A348279 * A348281 A348282 A348283

Keyword

nonn

Author

Wesley Ivan Hurt, Oct 09 2021

Status

approved