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A227153 Product of nonzero digits of n in factorial base.

%I A227153 #38 May 23 2025 01:12:46
%S A227153 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,
%T A227153 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,
%U A227153 6,6,12,12,3,3,3,3,6,6,3,3,3,3,6,6,6,6,6,6
%N A227153 Product of nonzero digits of n in factorial base.
%C A227153 a(0) = 1 as an empty product always gives 1.
%H A227153 Antti Karttunen, <a href="/A227153/b227153.txt">Table of n, a(n) for n = 0..5040</a>
%F A227153 For all n, a(A227157(n)) = A208575(A227157(n)).
%t A227153 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 *)
%o A227153 (MIT/GNU Scheme)
%o A227153 (define (A227153 n) (apply * (delete-matching-items (n->factbase n) zero?)))
%o A227153 (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))))))
%o A227153 (Python)
%o A227153 from functools import reduce
%o A227153 from operator import mul
%o A227153 def A(n, p=2):
%o A227153     return n if n<p else A(n//p, p+1)*10 + n%p
%o A227153 def a(n):
%o A227153     return 1 if n<2 else reduce(mul, [int(i) for i in str(A(n)) if i!="0"])
%o A227153 print([a(n) for n in range(201)]) # _Indranil Ghosh_, Jun 19 2017
%o A227153 (Python)
%o A227153 def a(n, k=2): return max(n % k, 1) * a(n // k, k + 1) if n else 1 # _David Radcliffe_, May 22 2025
%Y A227153 A227157 gives the positions where equal with A208575.
%Y A227153 Cf. A007623, A227154, A227191.
%K A227153 nonn,base
%O A227153 0,5
%A A227153 _Antti Karttunen_, Jul 04 2013