OFFSET
1,1
COMMENTS
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
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 whose distinct parts form an initial interval with a single hole. The enumeration of these partitions by sum is given by A090858.
EXAMPLE
The sequence of terms together with their prime indices begins:
3: {2}
9: {2,2}
10: {1,3}
15: {2,3}
20: {1,1,3}
27: {2,2,2}
40: {1,1,1,3}
42: {1,2,4}
45: {2,2,3}
50: {1,3,3}
70: {1,3,4}
75: {2,3,3}
80: {1,1,1,1,3}
81: {2,2,2,2}
84: {1,1,2,4}
100: {1,1,3,3}
105: {2,3,4}
126: {1,2,2,4}
135: {2,2,2,3}
140: {1,1,3,4}
MATHEMATICA
Select[Range[100], Length[Complement[Range[PrimePi[FactorInteger[#][[-1, 1]]]], PrimePi/@First/@FactorInteger[#]]]==1&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 19 2019
STATUS
approved