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We parameterize solutions to the equality$\Phi_3(x)=\Phi_3(a_1)\Phi_3(a_2)\cdots\Phi_3(a_n)$ when each $\Phi_3(a_i)$ isprime. Our focus is on the special cases when $n=2,3,4$, as this analysissimplifies and extends bounds on the total number of prime factors of an oddperfect number.

Prime factors of $\Phi_3(x)$ of the same form