OFFSET
1,30
COMMENTS
By convention a(1) = 0.
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
EXAMPLE
The a(84) = 8 strict trees: (((42)1)1), (((41)2)1), ((4(21))1), ((421)1), (((41)1)2), ((41)(21)), ((41)21), (4(21)1).
MATHEMATICA
nn=120;
ptns=Table[If[n===1, {}, Join@@Cases[FactorInteger[n]//Reverse, {p_, k_}:>Table[PrimePi[p], {k}]]], {n, nn}];
tris=Join@@Map[Tuples[IntegerPartitions/@#]&, ptns];
qci[y_]:=qci[y]=If[Length[y]===1, 1, Sum[Times@@qci/@t, {t, Select[tris, And[Length[#]>1, Sort[Join@@#, Greater]===y, UnsameQ@@Total/@#]&]}]];
qci/@ptns
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 06 2018
STATUS
approved