These functions are defined for all natural numbers > 1 by: g(x) = Sum (p_j^k_j) where x = Product (p_j^k_j) is prime factorization of x (A008475); f(n) = max{x:g(x)=n} (A051703); m(n) = lcm(1,2,3,...,n) (A003418).
There are no more prime powers in the list <= 199. Conjecture: The sequence is finite, i.e., f(g(m(q))) > m(q) for sufficiently great prime powers q.
No other terms below 409. - Max Alekseyev, Sep 05 2023
