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.
EXAMPLE
The terms together with their prime indices begin:
4: {1,1} 38: {1,8} 77: {4,5}
6: {1,2} 39: {2,6} 82: {1,13}
9: {2,2} 40: {1,1,1,3} 84: {1,1,2,4}
10: {1,3} 46: {1,9} 85: {3,7}
12: {1,1,2} 49: {4,4} 86: {1,14}
14: {1,4} 51: {2,7} 87: {2,10}
15: {2,3} 55: {3,5} 91: {4,6}
21: {2,4} 57: {2,8} 93: {2,11}
22: {1,5} 58: {1,10} 94: {1,15}
25: {3,3} 62: {1,11} 95: {3,8}
26: {1,6} 63: {2,2,4} 106: {1,16}
30: {1,2,3} 65: {3,6} 111: {2,12}
33: {2,5} 69: {2,9} 112: {1,1,1,1,4}
34: {1,7} 70: {1,3,4} 115: {3,9}
35: {3,4} 74: {1,12} 118: {1,17}
MATHEMATICA
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Length[prix[#]]==2||MemberQ[prix[#], Total[prix[#]]/2]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 08 2023
STATUS
approved