Primordial-product numbers such that there are no triples (a,b,c) with all a+b+c = k1 and all a*b*c = k2, where k1 and k2 are two positive integers and k1 is prime.

2, 6, 30, 210, 2310, 30030, 262144, 510510, 4194304, 8388608, 9699690, 16777216, 223092870, 6469693230, 68719476736, 200560490130, 549755813888, 7420738134810, 35184372088832, 70368744177664

1

A primordial-product number is the product of primordial numbers. See A025487 for primordial numbers. This sequence appears to be the union of two sequences: product of consecutive primes (starting with 2) and sporadic powers of 2 (the exponents are listed in S000907).

T. D. Noe, Plot of 20 terms

(Mma) (* run the program in S000904 and then *) pri[[Flatten[Position[tAll, {0, 0}]]]]

nonn,hard

T. D. Noe, Jun 15 2016