# Phi-Pi-Po-Pum

For any positive integer $$n,$$ the Euler's totient function $$\phi(n)$$ is defined as the number of integers from $$1$$ to $$n$$ that are coprime to $$n.$$ We will call a positive integer $$m$$ infinitely Euler, if there exists an infinite sequence of positive integers $$m_1,m_2,m_3,...$$, such that $$m_1=m$$ and $$m_i=\phi(m_{i+1})$$ for all $$i\geq 1.$$ How many positive integers less than $$1000$$ are infinitely Euler?

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