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 A348280 a(n) = Sum_{d|n} n^(d'). 0

%I #11 Dec 31 2021 21:09:40

%S 1,3,4,261,6,7789,8,68719480841,531451,10000021,12,184884258895306009,

%T 14,20661046813,2562890656,340282366920938463463374888906744987665,18,

%U 229468251895129407175774597,20,16777216000000000000001280160041,16679880978244

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

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

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

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

%o a(n) = sumdiv(n, d, n^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 May 20 03:01 EDT 2024. Contains 372703 sequences. (Running on oeis4.)