Erdős's infinitude conjecture for Ruth–Aaron numbers

For a positive integer $n=\prod_{i=1}^k p_i^{a_i}$, define

$$f(n)=\sum_{i=1}^k a_i p_i.$$

A Ruth–Aaron number is an integer $n$ satisfying $f(n)=f(n+1)$. Erdős's infinitude conjecture. There are infinitely many integers $n$ such that

$$f(n)=f(n+1).$$

This is the named Erdős conjecture appearing in the paper's future-work discussion. The source gives examples and partial counting results but no proof or disproof of infinitude.