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: () 22: (5,1) 42: (4,2,1)
3: (2) 23: (9) 43: (14)
5: (3) 25: (3,3) 45: (3,2,2)
6: (2,1) 26: (6,1) 46: (9,1)
7: (4) 27: (2,2,2) 47: (15)
9: (2,2) 29: (10) 49: (4,4)
10: (3,1) 30: (3,2,1) 50: (3,3,1)
11: (5) 31: (11) 51: (7,2)
13: (6) 33: (5,2) 53: (16)
14: (4,1) 34: (7,1) 54: (2,2,2,1)
15: (3,2) 35: (4,3) 55: (5,3)
17: (7) 37: (12) 57: (8,2)
18: (2,2,1) 38: (8,1) 58: (10,1)
19: (8) 39: (6,2) 59: (17)
21: (4,2) 41: (13) 61: (18)
MATHEMATICA
ck[y_]:=With[{w=Count[y, 1]}, If[w==0, Max@@y, Count[y, _?(#>w&)]-w]];
Select[Range[100], ck[Reverse[Flatten[Cases[FactorInteger[#], {p_, k_}:>Table[PrimePi[p], {k}]]]]]>=0&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 09 2022
STATUS
approved