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