OFFSET
1,2
COMMENTS
The Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), giving a bijective correspondence between positive integers and integer partitions.
EXAMPLE
The sequence of terms together with their prime indices begins:
1: {} 81: {2,2,2,2}
3: {2} 90: {1,2,2,3}
4: {1,1} 100: {1,1,3,3}
9: {2,2} 108: {1,1,2,2,2}
10: {1,3} 120: {1,1,1,2,3}
12: {1,1,2} 144: {1,1,1,1,2,2}
16: {1,1,1,1} 160: {1,1,1,1,1,3}
25: {3,3} 192: {1,1,1,1,1,1,2}
27: {2,2,2} 225: {2,2,3,3}
30: {1,2,3} 243: {2,2,2,2,2}
36: {1,1,2,2} 250: {1,3,3,3}
40: {1,1,1,3} 256: {1,1,1,1,1,1,1,1}
48: {1,1,1,1,2} 270: {1,2,2,2,3}
64: {1,1,1,1,1,1} 300: {1,1,2,3,3}
75: {2,3,3} 324: {1,1,2,2,2,2}
MATHEMATICA
Select[Range[1000], EvenQ[Total[Cases[FactorInteger[#], {p_, k_}:>k*PrimePi[p]]]]&&Max@@First/@FactorInteger[#]<=Prime[3]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 16 2021
STATUS
approved