A085507 Stirling transform of the prime characteristic function.

0, 0, 1, 4, 13, 41, 136, 505, 2171, 10693, 58246, 340242, 2095435, 13492077, 90267633, 623383765, 4414350135, 31899350954, 235002008725, 1773013299342, 13855253098226, 114135759054965, 1010686200326760, 9744658443894282, 102153128291263124, 1147158516520205256

Offset: 0

Author

Eric W. Weisstein, Jul 02 2003

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..576
• S. K. Ghosal, J. K. Mandal, Stirling Transform Based Color Image Authentication, Procedia Technology, 2013 Volume 10, 2013, Pages 95-104.
• Eric Weisstein's World of Mathematics, Stirling Transform

Programs

Maple

b:= proc(n, m) option remember;
     `if`(n=0, `if`(isprime(m), 1, 0), m*b(n-1, m)+b(n-1, m+1))
    end:
a:= n-> b(n, 0):
seq(a(n), n=0..25);  # Alois P. Heinz, Aug 06 2021

Mathematica

a[n_] := Sum[ StirlingS2[n, k]*Boole[PrimeQ[k]], {k, 0, n}]; Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Oct 29 2012 *)

Formula

G.f.: Sum_{k>=1} x^prime(k)/Product_{j=1..prime(k)} (1 - j*x). - Ilya Gutkovskiy, Jun 19 2018