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A257686 a(0) = 0, for n >= 1: a(n) = A099563(n) * A048764(n).

%I A257686 #28 May 08 2021 11:22:58
%S A257686 0,1,2,2,4,4,6,6,6,6,6,6,12,12,12,12,12,12,18,18,18,18,18,18,24,24,24,
%T A257686 24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,48,48,
%U A257686 48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,72
%N A257686 a(0) = 0, for n >= 1: a(n) = A099563(n) * A048764(n).
%C A257686 For n >= 1, a(n) = the smallest term of A051683 >= n.
%C A257686 Can also be obtained by replacing with zeros all other digits except the first (the most significant) in the factorial base representation of n (A007623), then converting back to decimal.
%C A257686 Useful when computing A257687.
%H A257686 Antti Karttunen, <a href="/A257686/b257686.txt">Table of n, a(n) for n = 0..5040</a>
%F A257686 a(0) = 0, and for n >= 1: a(n) = A099563(n) * A048764(n).
%F A257686 Other identities:
%F A257686 For all n >= 0, a(n) = n - A257687(n).
%F A257686 a(n) = A000030(A007623(n))*(A055642(A007623(n)))! - _Indranil Ghosh_, Jun 21 2017
%e A257686 Factorial base representation (A007623) of 2 is "10", zeroing all except the most significant digit does not change anything, thus a(2) = 2.
%e A257686 Factorial base representation (A007623) of 3 is "11", zeroing all except the most significant digit gives "10", thus a(3) = 2.
%e A257686 Factorial base representation of 23 is "321", zeroing all except the most significant digit gives "300" which is factorial base representation of 18, thus a(23) = 18.
%o A257686 (Scheme) (define (A257686 n) (if (zero? n) n (* (A099563 n) (A048764 n))))
%o A257686 (Python)
%o A257686 from sympy import factorial as f
%o A257686 def a007623(n, p=2): return n if n<p else a007623(n//p, p+1)*10 + n%p
%o A257686 def a(n):
%o A257686     x=str(a007623(n))
%o A257686     return int(x[0])*f(len(x))
%o A257686 print([a(n) for n in range(201)]) # _Indranil Ghosh_, Jun 21 2017
%Y A257686 Cf. A007623, A048764, A051683, A099563, A257687.
%Y A257686 Cf. also A053644 (analogous sequence for base-2).
%K A257686 nonn,base
%O A257686 0,3
%A A257686 _Antti Karttunen_, May 04 2015