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A375774 The number of n-digit integers that can be written as the product of n single-digit integers. The single-digit integers need not be distinct.

%I A375774 #13 Sep 08 2024 08:26:20
%S A375774 10,27,55,85,108,119,118,108,94,78,60,46,35,27,19,14,10,7,4,2,1,0,0,0,
%T A375774 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A375774 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A375774 The number of n-digit integers that can be written as the product of n single-digit integers. The single-digit integers need not be distinct.
%C A375774 a(21)=1 (9^21 has 21 digits). For all n>21, a(n)=0.
%H A375774 <a href="/index/Con#constant">Index entries for eventually constant sequences</a>
%e A375774 a(2) is 27 because 27 2-digit integers can be written as the product of 2 single-digit integers. Those 27 integers are: 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32, 35, 36, 40, 42, 45, 48, 49, 54, 56, 63, 64, 72 and 81. Note that each of the 2-digit integers 12, 16, 18, 24 and 36 can be expressed as a product of 2 single-digit integers in more than 1 way. However, each of those 2-digit integers is only counted once.
%o A375774 (Python)
%o A375774 from math import prod
%o A375774 from itertools import combinations_with_replacement as cwr
%o A375774 def a(n):
%o A375774     if n > 21: return 0
%o A375774     L, U = (n>1)*10**(n-1)-1, 10**n
%o A375774     return len(set(p for mc in cwr(range(10), n) if L < (p:=prod(mc)) < U))
%o A375774 print([a(n) for n in range(1, 22)]) # _Michael S. Branicky_, Aug 27 2024
%Y A375774 Cf. A366181.
%K A375774 nonn,base
%O A375774 1,1
%A A375774 _Clive Tooth_, Aug 27 2024