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: () 24: (2,1,1,1) 47: (15)
3: (2) 25: (3,3) 48: (2,1,1,1,1)
5: (3) 26: (6,1) 49: (4,4)
6: (2,1) 28: (4,1,1) 50: (3,3,1)
7: (4) 29: (10) 52: (6,1,1)
10: (3,1) 31: (11) 53: (16)
11: (5) 34: (7,1) 55: (5,3)
12: (2,1,1) 35: (4,3) 56: (4,1,1,1)
13: (6) 37: (12) 58: (10,1)
14: (4,1) 38: (8,1) 59: (17)
17: (7) 40: (3,1,1,1) 61: (18)
19: (8) 41: (13) 62: (11,1)
20: (3,1,1) 43: (14) 65: (6,3)
22: (5,1) 44: (5,1,1) 67: (19)
23: (9) 46: (9,1) 68: (7,1,1)
MATHEMATICA
pq[y_]:=Length[Select[Range[Length[y]], #==y[[#]]&]];
Select[Range[100], pq[Reverse[Flatten[Cases[FactorInteger[#], {p_, k_}:>Table[PrimePi[p], {k}]]]]]==0&]
CROSSREFS
* = unproved
The complement is A352827.
*A001522 counts partitions with a fixed point.
A122111 represents partition conjugation using Heinz numbers.
A352833 counts partitions by fixed points.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 06 2022
STATUS
approved