A208575 Product of digits of n in factorial base.

0, 1, 0, 1, 0, 2, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 3, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 3, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 4, 0, 8, 0, 0, 0, 6, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 6, 0, 0, 0, 6, 0, 12, 0, 0, 0, 9, 0, 18

Offset: 0

Author

Charles R Greathouse IV, Feb 28 2012

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10080
• M. R. Diamond and D. D. Reidpath, A counterexample to conjectures by Sloane and Erdős concerning the persistence of numbers, Journal of Recreational Mathematics 29:2 (1998), pp. 89-92.
• Index entries for sequences related to factorial base representation

Crossrefs

Cf. A007623, A007954, A031346, A208576, A208277, A227153, A227154, A286590.

Programs

Mathematica

(* For the definition of the factorial base version of IntegerDigits, see A007623 *) Table[Times@@factBaseIntDs[n], {n, 0, 99}] (* Alonso del Arte, Feb 28 2012 *)

PARI

a(n)=my(k=1,s=1);while(n,s*=n%k++;n\=k);s

Python

from functools import reduce
from operator import mul
def A(n, p=2):
    return n if n
Indranil Ghosh, Jun 19 2017