Erdős Problem #964 — Dense ratios of consecutive divisor counts

About 40 years old · traced to 1986

Let $τ(n)$ denote the number of positive divisors of $n$ . Is the sequence $τ(n+1)/τ(n)$ dense in $(0,∞)$ ?

References

Primary source

P. Erdős, Some problems on number theory, Proceedings of the Seventeenth Southeastern International Conference on Combinatorics, Graph Theory, and Computing (1986), 225–244.

Additional references

P. Erdős, Some problems on number theory, Proceedings of the Seventeenth Southeastern International Conference on Combinatorics, Graph Theory, and Computing (1986), 225–244.

divisors number-theory

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