Re: Can you provide some more details on what you are trying to do?

If L+(P,N0) is the set of functions f: P -> N0 with the property that

there exists {n0 in N0} such that for all {p in P} {p >= n0 --> f(p)=0}

then there exists a bijection N1 -> L+(P,N0) such that if n -> f then

n = PRODUCT {p in P} p^{f(p)}

Here P is the set of prime numbers and N1= N0 ~ {0}