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 A007294.
EXAMPLE
The sequence of terms together with their prime indices begins:
1: {}
2: {1}
4: {1,1}
5: {3}
8: {1,1,1}
10: {1,3}
13: {6}
16: {1,1,1,1}
20: {1,1,3}
25: {3,3}
26: {1,6}
29: {10}
32: {1,1,1,1,1}
40: {1,1,1,3}
47: {15}
50: {1,3,3}
52: {1,1,6}
58: {1,10}
64: {1,1,1,1,1,1}
65: {3,6}
MATHEMATICA
nn=1000;
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
trgs=Table[n*(n+1)/2, {n, Sqrt[2*PrimePi[nn]]}];
Select[Range[nn], SubsetQ[trgs, primeMS[#]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 02 2019
STATUS
approved