%I #16 Mar 09 2024 11:17:26
%S 1,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,2,2,3,2,
%T 3,3,3,3,3,3,2,2,3,3,2,3,3,3,3,3,2,2,3,3,3,2,3,3,3,3,2,2,3,3,3,3,2,3,
%U 3,3,2,2,3,3,3,3,3,2,3,3,2,2,3,3,3,3,3,3,2,3,2
%N a(n) is the number of distinct products of nonempty submultisets of the digits of n.
%C a(n) <= A000005(A051801(n)). - _David A. Corneth_, Mar 05 2024
%H David A. Corneth, <a href="/A364136/b364136.txt">Table of n, a(n) for n = 0..10000</a>
%e n = 10: products of digits are {0, 1, 0*1}, distinct products of digits are {0, 1}, thus a(10) = 2.
%e n = 11: products of digits are {1, 1*1}, distinct product of digits is {1}, thus a(11) = 1.
%e n = 23: products of digits are {2, 3, 2*3}, distinct products of digits are {2, 3, 6}, thus a(23) = 3.
%o (PARI) a(n) = {if(n==0, return(1));
%o my(d = vecsort(digits(n)), l = List());
%o for(i = 1, #d,
%o forvec(x = vector(i, j, [1,#d]),
%o c = vecprod(vector(i, j, d[x[j]]));
%o listput(l, c)
%o ,
%o 2
%o )
%o );
%o #Set(l)
%o } \\ _David A. Corneth_, Mar 05 2024
%Y Cf. A000005, A007954, A051801, A055642, A360391.
%K base,nonn
%O 0,11
%A _Ctibor O. Zizka_, Jul 10 2023