2025/06/05 by Kovač, Vjekoslav, Luca, Florian
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2506.04883
Denote f(n):=∑1≤ k≤ n τ(2k-1), where τ is the number of divisors function. Motivated by a question of Paul Erdős, we show that the sequence of ratios f(2n)/f(n) is unbounded. We also present conditional results on the divergence of this sequence to infinity. Finally, we test numerically both the conjecture f(2n)/f(n)→∞ and our sufficient conditions for it to hold.