On the Number of Divisors of Mersenne Numbers
Abstract
Denote f(n):=∑1⩽k⩽nτ(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 give experimental evidence on both the conjecture f(2n)/f(n)→∞ and our sufficient conditions for it to hold.
Fields of Study & Subjects
Analytic Number Theory Research
Advanced Mathematical Theories
Advanced Mathematical Identities
Publication details
- Journal / source
- Experimental Mathematics
- Publisher
- Informa UK Limited
- Pages
- 1–24
- Publication date
- 20 May 2026
- Language
- EN