Are there infinitely many even integers $n$ such that $1+4\varphi(n)$ is a perfect square?

Question

Let $\varphi(n)$ the Euler's totient function. The sequence of even integers $n$ such that $$1+4\varphi(n)$$ is a perfect square starts as $$4, 6, 14, 18, 26, 28, 36, 42, 44, 50\ldots$$

Question. I've curiosity about this question: are there infinitely many even integers $n$ such that $1+4\varphi(n)$ is a perfect square? Many thanks.

Answer 1

Yes. Let $p>2$ be a prime. Then $\phi(2p^2)=p(p-1)$ and thus $$ 1+4\phi(2p^2)=1+4p(p-1)=(2p-1)^2. $$