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.
The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).
EXAMPLE
The terms together with their prime indices begin:
3: {2} 23: {9} 42: {1,2,4}
5: {3} 25: {3,3} 43: {14}
6: {1,2} 26: {1,6} 45: {2,2,3}
7: {4} 27: {2,2,2} 46: {1,9}
9: {2,2} 29: {10} 47: {15}
10: {1,3} 30: {1,2,3} 49: {4,4}
11: {5} 31: {11} 50: {1,3,3}
13: {6} 33: {2,5} 51: {2,7}
14: {1,4} 34: {1,7} 53: {16}
15: {2,3} 35: {3,4} 54: {1,2,2,2}
17: {7} 36: {1,1,2,2} 55: {3,5}
18: {1,2,2} 37: {12} 57: {2,8}
19: {8} 38: {1,8} 58: {1,10}
21: {2,4} 39: {2,6} 59: {17}
22: {1,5} 41: {13} 60: {1,1,2,3}
MATHEMATICA
prifacs[n_]:=If[n==1, {}, Flatten[ConstantArray@@@FactorInteger[n]]];
Select[Range[100], Median[prifacs[#]]>2&]
CROSSREFS
These partitions are counted by A238495.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 14 2023
STATUS
approved