A360391 a(n) is the number of distinct sums of nonempty subsets of the digits of n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 2

Offset: 0

Author

Ctibor O. Zizka, Feb 06 2023

Keywords

• nonn
• base

Comments

1 <= a(n) <= 2^(1 + floor(log_10(n))) - 1.

Examples

			k = 10: sums of digits are {0, 1, 0 + 1}, distinct sums of digits are {0, 1}, thus a(10) = 2.
k = 11: sums of digits are {1, 1 + 1}, distinct sums of digits are {1, 2}, thus a(11) = 2.
k = 12: sums of digits are {1, 2, 1 + 2}, distinct sums of digits are {1, 2, 3}, thus a(12) = 3.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A007953, A043562, A054054, A054055, A055642.

Programs

Mathematica

a[n_] := Length[Union[Total /@ Select[Subsets[IntegerDigits[n]], # != {} &]]]; Array[a, 100, 0] (* Amiram Eldar, Feb 06 2023 *)

Python

from itertools import combinations as C
def a(n):
    v = list(map(int, str(n)))
    return len(set(sum(c) for r in range(1, len(v)+1) for c in C(v, r)))
print([a(n) for n in range(89)]) # Michael S. Branicky, Feb 19 2023