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: ()
2: (1)
6: (2,1)
9: (2,2)
10: (3,1)
12: (2,1,1)
15: (3,2)
18: (2,2,1)
20: (3,1,1)
30: (3,2,1)
35: (4,3)
49: (4,4)
54: (2,2,2,1)
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
conj[y_]:=If[Length[y]==0, y, Table[Length[Select[y, #>=k&]], {k, 1, Max[y]}]];
Select[Range[100], Count[conj[primeMS[#]], _?OddQ]==Count[primeMS[#], _?OddQ]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 28 2022
STATUS
approved