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

%I A360391 #33 Feb 19 2023 18:43:54
%S A360391 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,
%T A360391 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,
%U A360391 3,3,2,3,3,3,3,3,3,2,3,3,2,3,3,3,3,3,3,3,2
%N A360391 a(n) is the number of distinct sums of nonempty subsets of the digits of n.
%C A360391 1 <= a(n) <= 2^(1 + floor(log_10(n))) - 1.
%H A360391 Michael S. Branicky, <a href="/A360391/b360391.txt">Table of n, a(n) for n = 0..10000</a>
%e A360391 k = 10: sums of digits are {0, 1, 0 + 1}, distinct sums of digits are {0, 1}, thus a(10) = 2.
%e A360391 k = 11: sums of digits are {1, 1 + 1}, distinct sums of digits are {1, 2}, thus a(11) = 2.
%e A360391 k = 12: sums of digits are {1, 2, 1 + 2}, distinct sums of digits are {1, 2, 3}, thus a(12) = 3.
%t A360391 a[n_] := Length[Union[Total /@ Select[Subsets[IntegerDigits[n]], # != {} &]]]; Array[a, 100, 0] (* _Amiram Eldar_, Feb 06 2023 *)
%o A360391 (Python)
%o A360391 from itertools import combinations as C
%o A360391 def a(n):
%o A360391     v = list(map(int, str(n)))
%o A360391     return len(set(sum(c) for r in range(1, len(v)+1) for c in C(v, r)))
%o A360391 print([a(n) for n in range(89)]) # _Michael S. Branicky_, Feb 19 2023
%Y A360391 Cf. A007953, A043562, A054054, A054055, A055642.
%K A360391 nonn,base
%O A360391 0,11
%A A360391 _Ctibor O. Zizka_, Feb 06 2023