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A258652 Sum of the k-th arithmetic derivative of n-k for k=0..n. 2
0, 1, 2, 4, 5, 9, 11, 16, 14, 25, 36, 59, 99, 209, 419, 860, 1730, 3862, 9464, 21868, 74371, 244648, 727345, 3098351, 13469007, 56269849, 281642632, 1406177909, 9597415332, 58891421656, 411673964638, 3406742649805, 24202753250241, 176482943622608 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Jun 01 2018, from Maple *)

CROSSREFS

Antidiagonal sums of A258651.

Cf. A003415.

Sequence in context: A113755 A124254 A192615 * A065514 A152186 A085765

Adjacent sequences:  A258649 A258650 A258651 * A258653 A258654 A258655

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 06 2015

STATUS

approved

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Last modified November 13 00:25 EST 2019. Contains 329083 sequences. (Running on oeis4.)