OFFSET
1,2
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).
EXAMPLE
The sequence of terms together with their prime indices begins:
1: {}
3: {2}
5: {3}
7: {4}
9: {2,2}
11: {5}
13: {6}
17: {7}
19: {8}
21: {2,4}
23: {9}
25: {3,3}
27: {2,2,2}
29: {10}
31: {11}
33: {2,5}
35: {3,4}
37: {12}
41: {13}
43: {14}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[1, 100, 2], Intersection[primeMS[#], Union@@primeMS/@primeMS[#]]=={}&]
CROSSREFS
The subset version is A324742, with maximal case A324763. The strict integer partition version is A324752. The integer partition version is A324757. An infinite version is A324695.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 17 2019
STATUS
approved