Q: Let f(n) denote the sum of the distinct prime divisors of the positive integer n and let d(n) denote the
number of divisors of n. (So, for example, f(12) = 2 + 3 = 5 and d(12) = 6 since the divisors of 12 are 1,
2, 3, 4, 6, and 12.)
Are there infinitely many n such that nf(n) + d(n) is twice a perfect square?