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A348376
a(n) = Sum_{k=1..n} n^(k'), where ' is the arithmetic derivative.
0
1, 3, 7, 265, 641, 9091, 19237, 68719513633, 282430133569, 1000011110041, 3138449811201, 184893175034572093, 665439907336277581, 2178010052496312581, 6568538143240091341, 340282366920938463481821633053755244641, 2367911594760467245892768071944854959281
OFFSET
1,2
MAPLE
a:= n-> add(n^(k*add(i[2]/i[1], i=ifactors(k)[2])), k=1..n):
seq(a(n), n=1..18); # Alois P. Heinz, Oct 15 2021
MATHEMATICA
d[0] = d[1] = 0; d[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); a[n_] := Sum[n^d[k], {k, 1, n}]; Array[a, 20] (* Amiram Eldar, Oct 16 2021 *)
PROG
(PARI) ad(n) = vecsum([n/f[1]*f[2]|f<-factor(n+!n)~]); \\ A003415
a(n) = sum(k=1, n, n^ad(k)); \\ Michel Marcus, Oct 18 2021
CROSSREFS
Cf. A003415.
Sequence in context: A206333 A088097 A064774 * A089689 A248701 A103317
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Oct 15 2021
STATUS
approved