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A348278 a(n) = Sum_{d|n} d^(d'). 0
1, 3, 4, 259, 6, 7782, 8, 68719476995, 531445, 10000008, 12, 184884258895044454, 14, 20661046794, 2562890634, 340282366920938463463374607500487688451, 18, 229468251895129407140411991, 20, 16777216000000000000000010000264, 16679880978212 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Oct 09 2021
STATUS
approved

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Last modified May 24 13:16 EDT 2024. Contains 372773 sequences. (Running on oeis4.)