A227153 Product of nonzero digits of n in factorial base.

1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 4, 4, 3, 3, 3, 3, 6, 6, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 4, 4, 3, 3, 3, 3, 6, 6, 2, 2, 2, 2, 4, 4, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 8, 8, 6, 6, 6, 6, 12, 12, 3, 3, 3, 3, 6, 6, 3, 3, 3, 3, 6, 6, 6, 6, 6, 6

Offset: 0

Author

Antti Karttunen, Jul 04 2013

Keywords

• nonn
• base

Comments

a(0) = 1 as an empty product always gives 1.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..5040

Crossrefs

A227157 gives the positions where equal with A208575.

Cf. A007623, A227154, A227191.

Programs

Mathematica

a[n_] := Module[{k = n, m = 2, r, p = 1}, While[{k, r} = QuotientRemainder[k, m]; k != 0|| r != 0, If[r > 0, p *= r]; m++]; p]; Array[a, 100, 0] (* Amiram Eldar, Feb 07 2024 *)

Python

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

Python

def a(n, k=2): return max(n % k, 1) * a(n // k, k + 1) if n else 1 # David Radcliffe, May 22 2025

Formula

For all n, a(A227157(n)) = A208575(A227157(n)).