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

0,5

Comments

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

Links

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

Formula

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

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 *)

Prog

(Scheme)
(define (A227153 n) (apply * (delete-matching-items (n->factbase n) zero?)))
(define (n->factbase n) (let loop ((n n) (fex (if (zero? n) (list 0) (list))) (i 2)) (cond ((zero? n) fex) (else (loop (floor->exact (/ n i)) (cons (modulo n i) fex) (1+ i))))))
(Python)
from functools import reduce
from operator import mul
def A(n, p=2):
    return n if n<p else A(n//p, p+1)*10 + n%p
def a(n):
    return 1 if n<2 else reduce(mul, [int(i) for i in str(A(n)) if i!="0"])
print([a(n) for n in range(201)]) # 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

Crossrefs

A227157 gives the positions where equal with A208575.

Cf. A007623, A227154, A227191.

Sequence in context: A328114 A343504 A328582 * A328581 A238643 A140193

Adjacent sequences: A227150 A227151 A227152 * A227154 A227155 A227156

Keyword

nonn,base

Author

Antti Karttunen, Jul 04 2013

Status

approved