A number theory problem by Madhavarapu Revanth

Numbers with 6 factors are of the form $p^5$ or $p^2q$ where $p$ and $q$ are distinct primes. Hence the two-digit numbers of this form are:

• $p^5$ for $p = 2$

• $4q$ for $q \in \{3,5,7,11,13,17,19,23\}$

• $9q$ for $q \in \{2,5,7,11\}$

• $25q$ for $q \in \{2,3\}$

• $49q$ for $q = 2$

This gives us an answer of $1 + 8 + 4 + 2 + 1 = \boxed{16}$ .