kourovka.«19.25»

Let $G$ and $H$ be finite groups of the same order with $\sum_{g \in G} \phi(|g|) = \sum_{h \in H} \phi(|h|)$, where $\phi$ is the Euler totient function. Suppose that $G$ is simple. Is $H$ necessarily simple?

theorem kourovka.«19.25» : answer(sorry) ↔
    ∀ (G H : Type) [Group G] [Group H] [Fintype G] [Fintype H],
       ∑ g : G, φ (orderOf g) = ∑ h : H, φ (orderOf h) →
       IsSimpleGroup G → IsSimpleGroup H

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