A258845 The pi-based arithmetic derivative of n!.
0, 0, 1, 7, 52, 332, 2832, 22704, 242112, 2662848, 30620160, 354965760, 5057925120, 68627036160, 1054183818240, 17469144806400, 321351896678400, 5609441772748800, 112707637036646400, 2192664093342105600, 47745925079924736000, 1065919878891012096000
Offset: 0
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..450
Programs
-
Maple
with(numtheory): d:= n-> n*add(i[2]*pi(i[1])/i[1], i=ifactors(n)[2]): a:= proc(n) option remember; `if`(n<2, 0, a(n-1)*n+(n-1)!*d(n)) end: seq(a(n), n=0..25); -
Mathematica
d[n_] := n*Sum[i[[2]]*PrimePi[i[[1]]]/i[[1]], {i, FactorInteger[n]}]; a[n_] := a[n] = If[n < 2, 0, a[n-1]*n + (n-1)!*d[n]]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Mar 24 2017, translated from Maple *)