Would someone be so kind as to enlighten me as to whether the integer partition function, p(N), can be (or has been) inverted and where the inversion is recorded? I'm trying to avoid reinventing the wheel, so to speak; I've searched quite awhile and no luck (this function's inversion seems possible on the face of it).

[For those unfamiliar, the partition function, p(N), is that function which generates the characteristic number of integer partitions unique to every positive integer. For example, p(4) = 5 because the number 4 can be expressed as a sum of integers in 5 non-duplicated ways: (1 + 1 + 1 + 1), (1 + 1 + 2), (1 + 3), (2 + 2), and (4). One can view Rademacher's refinement of the Hardy-Ramanujan formula here ]

I tried to crunch the inversion using Mathematica and Maple, but both symbol processors returned null (I'm not the best at using them). I didn't get anywhere even when I attempted the inversion of alternative representations of p(N) such as that found in "Simple alternative to the Hardy-Ramanujan-Rademacher formula for p(N)" by N.M. Chase.

What resources might be helpful? My apologies if I have missed something elementary.