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A286606 a(n) = n mod product of nonzero digits of n in factorial base.

%I A286606 #19 Feb 21 2024 01:20:37
%S A286606 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,
%T A286606 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,
%U A286606 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
%N A286606 a(n) = n mod product of nonzero digits of n in factorial base.
%H A286606 Antti Karttunen, <a href="/A286606/b286606.txt">Table of n, a(n) for n = 1..10080</a>
%H A286606 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>.
%F A286606 a(n) = n mod A227153(n).
%t A286606 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 *)
%o A286606 (Scheme) (define (A286606 n) (modulo n (A227153 n)))
%o A286606 (Python)
%o A286606 from operator import mul
%o A286606 from functools import reduce
%o A286606 def a007623(n, p=2): return n if n<p else a007623(n//p, p+1)*10 + n%p
%o A286606 def a(n):
%o A286606     x=str(a007623(n)).replace('0', '')
%o A286606     return n%reduce(mul, map(int, x))
%o A286606 print([a(n) for n in range(1, 201)]) # _Indranil Ghosh_, Jun 21 2017
%Y A286606 Cf. A227153, A286604.
%K A286606 nonn,base
%O A286606 1,20
%A A286606 _Antti Karttunen_, Jun 18 2017