Erdős problem 946 · problems.science

There are infinitely many $n$ such that $τ(n) = τ(n+1)$ . Proved in [He84]. Here τ is the divisor counting function, which is σ 0 in mathlib.

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5 retained statements2415f78e850a

FormalConjectures/ErdosProblems/

946.lean

Retained formal statement2 of 5

The number of $n \le x$ with $τ(n) = τ(n+1)$ is at least $x / (\log x)^7$ for all sufficiently large $x$ . Proved in [He84].

FormalConjectures/ErdosProblems/946.leanErdos946.erdos_946.variants.heathbrown_lower_bound1 lineExact file

1(fun x => x / Real.log x ^ 7) =O[Filter.atTop] Erdos946.erdos946Count

SolvedStatement only, no proof