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A348278 a(n) = Sum_{d|n} d^(d'). 0

%I #11 Dec 31 2021 21:14:24

%S 1,3,4,259,6,7782,8,68719476995,531445,10000008,12,184884258895044454,

%T 14,20661046794,2562890634,340282366920938463463374607500487688451,18,

%U 229468251895129407140411991,20,16777216000000000000000010000264,16679880978212

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

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

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

%o (PARI) ad(n) = vecsum([n/f[1]*f[2]|f<-factor(n+!n)~]); \\ A003415

%o a(n) = sumdiv(n, d, d^ad(d)); \\ _Michel Marcus_, Oct 10 2021

%Y Cf. A003415 (arithmetic derivative).

%K nonn

%O 1,2

%A _Wesley Ivan Hurt_, Oct 09 2021

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Last modified June 21 13:19 EDT 2024. Contains 373544 sequences. (Running on oeis4.)