Name: "No powers as partition numbers"

There are no partition numbers $p(k)$ of the form $x^m$, with $x,m$ integers $>1$.

Reference: A41

def OeisA41.p (n : ℕ) : ℕ

The n-th partition number.

Equations

• OeisA41.p n = Fintype.card n.Partition

theorem OeisA41.noPowerPartitionNumber : sorry ↔ ∀ (k : ℕ), ¬(p k).IsPerfectPower

There are no partition numbers $p(k)$ of the form $x^m$, with $x,m$ integers $>1$. See comment by Zhi-Wei Sun (Dec 02 2013).