OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..100
Wikipedia, Arithmetic derivative
FORMULA
a(n) = Sum_{k=0..n} A258651(n-k,k).
MAPLE
d:= n-> n*add(i[2]/i[1], i=ifactors(n)[2]):
A:= proc(n, k) option remember; `if`(k=0, n, d(A(n, k-1))) end:
a:= proc(n) option remember; add(A(h, n-h), h=0..n) end:
seq(a(n), n=0..40);
MATHEMATICA
d[n_ /; n>1] := n*Sum[i[[2]]/i[[1]], {i, FactorInteger[n]}]; d[_] = 0;
A[n_, k_] := A[n, k] = If[k == 0, n, d[A[n, k-1]]];
a[n_] := a[n] = Sum[A[h, n-h], {h, 0, n}];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Jun 01 2018, from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 06 2015
STATUS
approved