OFFSET
1,1
COMMENTS
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are numbers whose maximum prime index divides their sum of prime indices.
The enumeration of these partitions by sum is given by A067538.
EXAMPLE
The sequence of terms together with their prime indices begins:
2: {1}
3: {2}
4: {1,1}
5: {3}
7: {4}
8: {1,1,1}
9: {2,2}
11: {5}
12: {1,1,2}
13: {6}
16: {1,1,1,1}
17: {7}
19: {8}
23: {9}
25: {3,3}
27: {2,2,2}
29: {10}
30: {1,2,3}
31: {11}
32: {1,1,1,1,1}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[200], Divisible[Total[primeMS[#]], Max[primeMS[#]]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 26 2019
STATUS
approved