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a(n) is the number of distinct products of nonempty submultisets of the digits of n.
1

%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