My aim with this information is to estimate how likely it is for an aliquot sequence with for example 2^4*3*c100 to lose/keep the 3 on the next iteration.

should be good enough especially if I can estimate the error.

Since I am using this for aliquot sequences I know certain factors do not divide the composite. In the case of 2^4*3*c100 this is 2 and 3(Note I could also do with doing things like 2^4*7 not just the first n primes. The exponent 4 isn't crucial as well.)