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%I #6 Apr 20 2024 10:49:21
%S 1,3,4,9,8,22,16,42,41,74,57,183,102,233
%N Row sums of A371783 and A371954 (k-quanimous partitions).
%C 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.
%t hwt[n_]:=Total[Cases[FactorInteger[n],{p_,k_}:>PrimePi[p]*k]];
%t facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&, Select[facs[n/d],Min@@#>=d&]], {d,Rest[Divisors[n]]}]];
%t Table[Sum[Length[Select[IntegerPartitions[n], Select[facs[Times@@Prime/@#], Length[#]==k&&SameQ@@hwt/@#&]!={}&]],{k,Divisors[n]}],{n,1,10}]
%Y Row sums of A371783.
%Y Row sums of A371954.
%Y A000005 counts divisors.
%Y A000041 counts integer partitions.
%Y A002219 (aerated) counts biquanimous partitions, ranks A357976.
%Y A321452 counts quanimous partitions, complement A321451.
%Y A371796 counts quanimous sets, differences A371797.
%Y Cf. A006827, A035470, A064914, A321455, A365543, A371737, A371791, A371795.
%K nonn,more
%O 1,2
%A _Gus Wiseman_, Apr 20 2024
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