OFFSET
1,1
COMMENTS
Also Heinz numbers of integer partitions (w,x,y) summing to n such that 2w = 3x + 4y, where the Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
EXAMPLE
The terms together with their prime indices begin:
66: {1,2,5}
153: {2,2,7}
266: {1,4,8}
609: {2,4,10}
806: {1,6,11}
1295: {3,4,12}
1599: {2,6,13}
1634: {1,8,14}
2107: {4,4,14}
3021: {2,8,16}
3055: {3,6,15}
3422: {1,10,17}
5254: {1,12,20}
5369: {4,6,17}
5795: {3,8,18}
5829: {2,10,19}
7138: {1,14,23}
8769: {2,12,22}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[1000], PrimeOmega[#]==3&&2*primeMS[#][[-1]]==3*primeMS[#][[-2]]+4*primeMS[#][[-3]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 02 2022
STATUS
approved