  Let $\sigma(n)$ and $\gamma(n)$ denote the sum of divisors and the product of
distinct prime divisors of $n$ respectively. We shall show that, if $n\neq 1,
1782$ and $\sigma(n)=(\gamma(n))^2$, then there exist odd (not necessarily
distinct) primes $p, p^\prime$ and (not necessarily odd) distinct primes $q_i
(i=1, 2, \ldots, k)$ such that $p, p^\prime\mid\mid n$, $q_i^2\mid\mid n (i=1,
2, \ldots, k)$ and $q_1\mid \sigma(p^2), q_{i+1}\mid\sigma(q_i^2) (1\leq i\leq
k-1), p^\prime \mid\sigma(q_k^2)$.
