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)
5: (3)
6: (2,1)
8: (1,1,1)
9: (2,2)
11: (5)
14: (4,1)
17: (7)
20: (3,1,1)
21: (4,2)
23: (9)
24: (2,1,1,1)
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[#]], _?EvenQ]==Count[primeMS[#], _?EvenQ]&]
CROSSREFS
These partitions are counted by A350948.
These are the positions of 0's in A350950.
A122111 = conjugation using Heinz numbers.
A316524 = alternating sum of prime indices.
The following rank partitions:
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 28 2022
STATUS
approved