A096371 Arithmetic derivative of n-th partition number.

0, 0, 1, 1, 1, 1, 1, 8, 13, 31, 41, 92, 18, 1, 162, 368, 131, 324, 167, 483, 299, 1788, 841, 256, 1905, 1179, 3680, 2607, 2769, 1383, 7484, 4065, 4664, 10101, 8627, 8030, 1, 5135, 10538, 55107, 42077, 25514, 31443, 90990, 33270, 46823, 89849, 106449, 70151

Offset: 0

Author

Reinhard Zumkeller, Jul 19 2004

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..3000

Programs

Maple

a:= n->(p->p*add(i[2]/i[1], i=ifactors(p)[2]))(combinat[numbpart](n)):
seq(a(n), n=0..100);  # Alois P. Heinz, Jun 04 2015

Mathematica

a[n_] := If[n<2, 0, Function[p, p*Sum[i[[2]]/i[[1]], {i, FactorInteger[p]}]][PartitionsP[n]]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Apr 04 2025, after Alois P. Heinz *)

Formula

a(n) = A003415(A000041(n)); a(A049575(n)) = 1.