A364136 a(n) is the number of distinct products of nonempty submultisets of the digits of n.

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, 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, 3, 3, 2, 2, 3, 3, 3, 3, 3, 2, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 2, 3, 2

Offset

0,11

Comments

a(n) <= A000005(A051801(n)). - David A. Corneth, Mar 05 2024

Links

David A. Corneth, Table of n, a(n) for n = 0..10000

Example

n = 10: products of digits are {0, 1, 0*1}, distinct products of digits are {0, 1}, thus a(10) = 2.
n = 11: products of digits are {1, 1*1}, distinct product of digits is {1}, thus a(11) = 1.
n = 23: products of digits are {2, 3, 2*3}, distinct products of digits are {2, 3, 6}, thus a(23) = 3.

Prog

(PARI) a(n) = {if(n==0, return(1));
	my(d = vecsort(digits(n)), l = List());
	for(i = 1, #d,
		forvec(x = vector(i, j, [1, #d]),
			c = vecprod(vector(i, j, d[x[j]]));
			listput(l, c)
		,
		2
		)
	);
	#Set(l)
} \\ David A. Corneth, Mar 05 2024

Crossrefs

Cf. A000005, A007954, A051801, A055642, A360391.

Sequence in context: A237684 A130634 A274828 * A257474 A257317 A163376

Adjacent sequences: A364133 A364134 A364135 * A364137 A364138 A364139

Keyword

base,nonn

Author

Ctibor O. Zizka, Jul 10 2023

Status

approved