Is it possible to create a function that gives the inverse of
pP[x_] := Sum[PrimePi[x^(1/k)]/k, {k, 1, Floor[Log2[x]]}]
i.e., a function that plots
{pP@#, #} & /@ Range@(InverseFunction[LogIntegral][100]) // ListLinePlot
but is a function in $n$ that gives the actual value of $\Pi^{-1}(n)$ for any $n?$
pP
only returns a set of discrete rational results. What should the inverse be if evaluated for anx
not in the set of allowable values? $\endgroup$