Let \(\mathfrak {p}_{\mathbb {P}_r}(n)\) denote the number of partitions of n into r-full primes. We use the Hardy–Littlewood circle method to find the asymptotic of \(\mathfrak {p}_{\mathbb {P}_r}(n)\) as \(n \rightarrow \infty \) . This extends previous results in the literature of partitions into primes. We also show an analogue result involving convolutions of von Mangoldt functions and the zeros of the Riemann zeta-function. To handle the resulting non-principal major arcs we introduce the definition of strange functions and pseudo-differentiability.
