Number Theory


Recurring Pairs of Consecutive Entries in the Number-of-Divisors Function

Authors: Richard J. Mathar

The Number-of-Divisors Function tau(n) is the number of divisors of a positive integer n, including 1 and n itself. Searching for pairs of the format (tau(n), tau(n+1)), some pairs appear (very) often, some never and some --- like (1,2), (4,9), or (10,3) --- exactly once. The manuscript provides proofs for 46 pairs to appear exactly once and lists 12 pairs that conjecturally appear only once. It documents a snapshot of a community effort to verify sequence A161460 of the Online Encyclopedia of Integer Sequences that started ten years ago.

Comments: 39 Pages.

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Submission history

[v1] 2019-11-17 08:18:55

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