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A372121 Row sums of A371783 and A371954 (k-quanimous partitions).

%I A372121 #10 Feb 13 2025 07:56:20
%S A372121 1,3,4,9,8,22,16,42,41,74,57,183,102,233,263,463,298,875,491,1350,
%T A372121 1172,1775,1256,4273,2225,4399,4584,8049,4566,14913,6843,18539,15831,
%U A372121 22894,18196,53323,21638,48947,50281,94500,44584,144976,63262,173436,169361,202153
%N A372121 Row sums of A371783 and A371954 (k-quanimous partitions).
%C A372121 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 A372121 hwt[n_]:=Total[Cases[FactorInteger[n],{p_,k_}:>PrimePi[p]*k]];
%t A372121 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&, Select[facs[n/d],Min@@#>=d&]], {d,Rest[Divisors[n]]}]];
%t A372121 Table[Sum[Length[Select[IntegerPartitions[n], Select[facs[Times@@Prime/@#], Length[#]==k&&SameQ@@hwt/@#&]!={}&]],{k,Divisors[n]}],{n,1,10}]
%o A372121 (PARI) T(n, d) = my(v=partitions(n/d), w=List([])); forvec(s=vector(d, i, [1, #v]), listput(w, vecsort(concat(vector(d, i, v[s[i]])))), 1); #Set(w);
%o A372121 a(n) = sumdiv(n, d, T(n, d)); \\ _Jinyuan Wang_, Feb 13 2025
%Y A372121 Row sums of A371783.
%Y A372121 Row sums of A371954.
%Y A372121 A000005 counts divisors.
%Y A372121 A000041 counts integer partitions.
%Y A372121 A002219 (aerated) counts biquanimous partitions, ranks A357976.
%Y A372121 A321452 counts quanimous partitions, complement A321451.
%Y A372121 A371796 counts quanimous sets, differences A371797.
%Y A372121 Cf. A006827, A035470, A064914, A321455, A365543, A371737, A371791, A371795.
%K A372121 nonn
%O A372121 1,2
%A A372121 _Gus Wiseman_, Apr 20 2024
%E A372121 More terms from _Jinyuan Wang_, Feb 13 2025