This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A208575 #31 Jul 06 2025 02:57:11
%S A208575 0,1,0,1,0,2,0,0,0,1,0,2,0,0,0,2,0,4,0,0,0,3,0,6,0,0,0,0,0,0,0,0,0,1,
%T A208575 0,2,0,0,0,2,0,4,0,0,0,3,0,6,0,0,0,0,0,0,0,0,0,2,0,4,0,0,0,4,0,8,0,0,
%U A208575 0,6,0,12,0,0,0,0,0,0,0,0,0,3,0,6,0,0,0,6,0,12,0,0,0,9,0,18
%N A208575 Product of digits of n in factorial base.
%H A208575 Antti Karttunen, <a href="/A208575/b208575.txt">Table of n, a(n) for n = 0..10080</a>
%H A208575 M. R. Diamond and D. D. Reidpath, <a href="https://www.mathe2.uni-bayreuth.de/sascha/oeis/persistence/PERSIST.PDF">A counterexample to conjectures by Sloane and Erdős concerning the persistence of numbers</a>, Journal of Recreational Mathematics 29:2 (1998), pp. 89-92.
%H A208575 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%t A208575 (* For the definition of the factorial base version of IntegerDigits, see A007623 *) Table[Times@@factBaseIntDs[n], {n, 0, 99}] (* _Alonso del Arte_, Feb 28 2012 *)
%o A208575 (PARI) a(n)=my(k=1,s=1);while(n,s*=n%k++;n\=k);s
%o A208575 (Python)
%o A208575 from functools import reduce
%o A208575 from operator import mul
%o A208575 def A(n, p=2):
%o A208575 return n if n<p else A(n//p, p+1)*10 + n%p
%o A208575 def a(n):
%o A208575 x=str(A(n - 1))
%o A208575 return 0 if "0" in x else reduce(mul, [int(i) for i in x])
%o A208575 print([a(n) for n in range(1, 101)]) # _Indranil Ghosh_, Jun 19 2017
%Y A208575 Cf. A007623, A007954, A031346, A208576, A208277, A227153, A227154, A286590.
%K A208575 nonn,base
%O A208575 0,6
%A A208575 _Charles R Greathouse IV_, Feb 28 2012