Let $1 = d_{1} < \dots < d_{τ (n)} = n$ be the divisors of $n$ and $G (n) = 1 \leq i < τ (n) \sum \frac{d _{i}}{d _{i + 1}} .$ Is it true that $G (n) \to \infty$ for almost all $n$ ? Can one prove an asymptotic formula for $\sum_{n \leq X} G (n)$ ?

Worked, still open.

number theory · solved · 0 attempts

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