OFFSET
1,2
COMMENTS
The Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). This gives a bijective correspondence between positive integers and integer partitions.
EXAMPLE
The terms together with their prime indices begin:
1: {}
3: {2}
9: {2,2}
21: {2,4}
22: {1,5}
27: {2,2,2}
63: {2,2,4}
76: {1,1,8}
81: {2,2,2,2}
117: {2,2,6}
147: {2,4,4}
175: {3,3,4}
186: {1,2,11}
189: {2,2,2,4}
243: {2,2,2,2,2}
MATHEMATICA
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
smu[y_]:=Union[Total/@Rest[Subsets[y]]];
nmz[y_]:=Complement[Range[Total[y]], Total/@Subsets[y]];
Select[Range[100], Length[smu[prix[#]]]==Length[nmz[prix[#]]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 25 2023
STATUS
approved