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:
2: {1}
6: {1,2}
20: {1,1,3}
36: {1,1,2,2}
56: {1,1,1,4}
176: {1,1,1,1,5}
240: {1,1,1,1,2,3}
416: {1,1,1,1,1,6}
864: {1,1,1,1,1,2,2,2}
1088: {1,1,1,1,1,1,7}
1344: {1,1,1,1,1,1,2,4}
2432: {1,1,1,1,1,1,1,8}
3200: {1,1,1,1,1,1,1,3,3}
5888: {1,1,1,1,1,1,1,1,9}
8448: {1,1,1,1,1,1,1,1,2,5}
14848: {1,1,1,1,1,1,1,1,1,10}
23040: {1,1,1,1,1,1,1,1,1,2,2,3}
31744: {1,1,1,1,1,1,1,1,1,1,11}
35840: {1,1,1,1,1,1,1,1,1,1,3,4}
39936: {1,1,1,1,1,1,1,1,1,1,2,6}
75776: {1,1,1,1,1,1,1,1,1,1,1,12}
MATHEMATICA
Select[Range[1000], Times@@Cases[If[#==1, {}, FactorInteger[#]], {p_, k_}:>PrimePi[p]^k]==PrimeOmega[#]&]
CROSSREFS
These partitions are counted by A353698.
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 19 2022
STATUS
approved