OFFSET
1,2
COMMENTS
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of integer partitions covering an initial interval of positive integers and containing all of their distinct multiplicities. The enumeration of these partitions by sum is given by A325707.
EXAMPLE
The sequence of terms together with their prime indices begins:
1: {}
2: {1}
6: {1,2}
12: {1,1,2}
18: {1,2,2}
30: {1,2,3}
36: {1,1,2,2}
60: {1,1,2,3}
90: {1,2,2,3}
120: {1,1,1,2,3}
150: {1,2,3,3}
180: {1,1,2,2,3}
210: {1,2,3,4}
270: {1,2,2,2,3}
300: {1,1,2,3,3}
360: {1,1,1,2,2,3}
420: {1,1,2,3,4}
450: {1,2,2,3,3}
540: {1,1,2,2,2,3}
600: {1,1,1,2,3,3}
MATHEMATICA
Select[Range[1000], #==1||Range[PrimeNu[#]]==PrimePi/@First/@FactorInteger[#]&&SubsetQ[PrimePi/@First/@FactorInteger[#], Last/@FactorInteger[#]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 18 2019
STATUS
approved