A348375 a(n) = Sum_{k=1..n} (n^k)' where ' is the arithmetic derivative.

0, 5, 34, 1252, 3711, 270605, 937924, 225978828, 2578767630, 76913580247, 310989720966, 154447492062352, 326011399456939, 107109225555230817, 3735502983248963648, 627025327447691781152, 875711370981239308953, 872019874471537450417269, 2082225625247428808306410

Offset

1,2

Links

Table of n, a(n) for n=1..19.

Example

a(4) = 1252; a(4) = Sum_{k=1..4} (4^k)' = (4^1)' + (4^2)' + (4^3)' + (4^4)' = 4' + 16' + 64' + 256' = 4 + 32 + 192 + 1024 = 1252.

Maple

a:= n-> add(n^k*add(i[2]/i[1], i=ifactors(n^k)[2]), k=1..n):
seq(a(n), n=1..19);  # Alois P. Heinz, Oct 15 2021

Mathematica

d[0] = d[1] = 0; d[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); a[n_] := Sum[d[n^k], {k, 1, n}]; Array[a, 20] (* Amiram Eldar, Oct 16 2021 *)

Crossrefs

Cf. A003415.

Sequence in context: A086345 A295545 A309534 * A194687 A208098 A216759

Adjacent sequences: A348372 A348373 A348374 * A348376 A348377 A348378

Keyword

nonn

Author

Wesley Ivan Hurt, Oct 15 2021

Status

approved