

A366529


Heinz numbers of integer partitions of even numbers with at least one even part.


2



3, 7, 9, 12, 13, 19, 21, 27, 28, 29, 30, 36, 37, 39, 43, 48, 49, 52, 53, 57, 61, 63, 66, 70, 71, 75, 76, 79, 81, 84, 87, 89, 90, 91, 101, 102, 107, 108, 111, 112, 113, 116, 117, 120, 129, 130, 131, 133, 138, 139, 144, 147, 148, 151, 154, 156, 159, 163, 165
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OFFSET

1,1


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.


LINKS



EXAMPLE

The terms together with their prime indices begin:
3: {2}
7: {4}
9: {2,2}
12: {1,1,2}
13: {6}
19: {8}
21: {2,4}
27: {2,2,2}
28: {1,1,4}
29: {10}
30: {1,2,3}
36: {1,1,2,2}
37: {12}
39: {2,6}
43: {14}
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], EvenQ[Total[prix[#]]]&&Or@@EvenQ/@prix[#]&]


CROSSREFS

The complement is counted by A047967.
Not requiring an even part gives A300061.
For odd instead of even we have A300063.
Not requiring even sum gives A324929.
Partitions of this type are counted by A366527.


KEYWORD

nonn


AUTHOR



STATUS

approved



