  Write $T(n)$ as the sum of the reciprocals of the primes which divide $n$.
Write $H(n) = \prod_{p|n}p/(p-1)$ where the product is over the prime divisors
of $n$. We prove new bounds for $T(n)$ and $H(n)$ in terms of the smallest
prime factor of $n$, under the assumption that $n$ is an odd perfect number.
Some of the results also apply under the weaker assumption that $n$ is odd and
primitive non-deficient.
