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1, 3, 4, 9, 8, 22, 16, 42, 41, 74, 57, 183, 102, 233
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internal format)
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OFFSET
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1,2
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COMMENTS
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A finite multiset of numbers is defined to be k-quanimous iff it can be partitioned into k multisets with equal sums. The triangles A371783 and A371954 count k-quanimous partitions.
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LINKS
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MATHEMATICA
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hwt[n_]:=Total[Cases[FactorInteger[n], {p_, k_}:>PrimePi[p]*k]];
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
Table[Sum[Length[Select[IntegerPartitions[n], Select[facs[Times@@Prime/@#], Length[#]==k&&SameQ@@hwt/@#&]!={}&]], {k, Divisors[n]}], {n, 1, 10}]
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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