OFFSET
0,8
COMMENTS
EXAMPLE
The binary indices of 119 are {1,2,3,5,6,7}, and the set partitions into blocks with the same sum are:
{{1,7},{2,6},{3,5}}
{{1,5,6},{2,3,7}}
{{1,2,3,6},{5,7}}
{{1,2,3,5,6,7}}
So a(119) = 3.
MATHEMATICA
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]& /@ sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
bix[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Table[Max[Length/@Select[sps[bix[n]], SameQ@@Total/@#&]], {n, 0, 100}]
CROSSREFS
A version for factorizations is A371733.
Positions of 1's are A371738.
Positions of terms > 1 are A371784.
A001055 counts factorizations.
A070939 gives length of binary expansion.
A326031 gives weight of the set-system with BII-number n.
A371783 counts k-quanimous partitions.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 14 2024
STATUS
approved