OFFSET
1,2
COMMENTS
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
The enumeration of these partitions by sum is given by A320348.
FORMULA
EXAMPLE
The sequence of terms together with their prime indices begins:
1: {}
2: {1}
4: {1,1}
8: {1,1,1}
12: {1,1,2}
16: {1,1,1,1}
18: {1,2,2}
24: {1,1,1,2}
32: {1,1,1,1,1}
48: {1,1,1,1,2}
54: {1,2,2,2}
64: {1,1,1,1,1,1}
72: {1,1,1,2,2}
96: {1,1,1,1,1,2}
108: {1,1,2,2,2}
128: {1,1,1,1,1,1,1}
144: {1,1,1,1,2,2}
162: {1,2,2,2,2}
192: {1,1,1,1,1,1,2}
256: {1,1,1,1,1,1,1,1}
288: {1,1,1,1,1,2,2}
324: {1,1,2,2,2,2}
360: {1,1,1,2,2,3}
384: {1,1,1,1,1,1,1,2}
MATHEMATICA
normQ[n_Integer]:=n==1||PrimePi/@First/@FactorInteger[n]==Range[PrimeNu[n]];
Select[Range[100], normQ[#]&&UnsameQ@@Last/@FactorInteger[#]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 01 2019
STATUS
approved