A286606 - OEIS

A286606

a(n) = n mod product of nonzero digits of n in factorial base.

0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 0, 4, 5, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 0, 4, 5, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 0, 1, 2, 3, 10, 11, 0, 1, 2, 0, 4, 5, 0, 1, 2, 0, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 2, 3, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 6, 7, 8, 9, 22, 23, 0

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OFFSET

1,20

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10080

Index entries for sequences related to factorial base representation.

FORMULA

a(n) = n mod A227153(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++]; Mod[n, p]]; Array[a, 100] (* Amiram Eldar, Feb 21 2024 *)

PROG

(Scheme) (define (A286606 n) (modulo n (A227153 n)))

(Python)

from operator import mul

from functools import reduce

def a007623(n, p=2): return n if n<p else a007623(n//p, p+1)*10 + n%p

def a(n):

x=str(a007623(n)).replace('0', '')

return n%reduce(mul, map(int, x))

print([a(n) for n in range(1, 201)]) # Indranil Ghosh, Jun 21 2017

CROSSREFS

Cf. A227153, A286604.