OFFSET
1,1
COMMENTS
These partitions are counted by A006477.
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:
6: {1,2}
12: {1,1,2}
14: {1,4}
15: {2,3}
18: {1,2,2}
24: {1,1,1,2}
26: {1,6}
28: {1,1,4}
30: {1,2,3}
33: {2,5}
35: {3,4}
36: {1,1,2,2}
38: {1,8}
42: {1,2,4}
45: {2,2,3}
48: {1,1,1,1,2}
MATHEMATICA
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Or@@EvenQ/@prix[#]&&Or@@OddQ/@prix[#]&]
CROSSREFS
These partitions are counted by A006477.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 16 2023
STATUS
approved