For the n-th primordial-product number p, the number of triples (a,b,c) with a+b+c = k1 and a*b*c = p, where k1 is a constant that is the least possible prime (or 0 if there are no primes).
0, 1, 0, 1, 1, 1, 1, 0, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 0, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 3, 2, 1, 2, 2, 2, 1, 3, 2, 1, 2, 1, 2, 1, 2, 3, 2, 2, 1, 1
1
Sequence S000904 lists the least primordial-product having a given number of triples. Sequence A025487 lists the primordial-product numbers.
T. D. Noe, Plot of 4425 terms
T. D. Noe, Table of 4425 terms
(Mma) (* run the program in S000904 and then *) Transpose[tAll][[1]]
nonn,hard
T. D. Noe, Jun 15 2016