A348361 a(n) = Sum_{k=1..n} k^(k'), where ' is the arithmetic derivative.

1, 3, 6, 262, 267, 8043, 8050, 68719484786, 68720016227, 68730016227, 68730016238, 184884327625052654, 184884327625052667, 184884348286099451, 184884350848990076, 340282366920938463463559491782617201532, 340282366920938463463559491782617201549, 340282366921167931715454621189757074317

Offset: 1

Author

Wesley Ivan Hurt, Oct 14 2021

Keywords

• nonn

Examples

			a(4) = 262; a(4) = Sum_{k=1..4} k^(k') = 1^(1') + 2^(2') + 3^(3') + 4^(4') = 1^0 + 2^1 + 3^1 + 4^4 = 262.
		

Crossrefs

Cf. A001923, A003415.

Programs

Maple

a:= n-> add(k^(k*add(i[2]/i[1], i=ifactors(k)[2])), k=1..n):
seq(a(n), n=1..18);  # Alois P. Heinz, Oct 14 2021

Mathematica

Accumulate@ Array[#^If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]]] &, 18] (* Michael De Vlieger, Oct 14 2021 *)