bibkey: huber2026a394407
authors: Felix Huber
year: 2026
title: "OEIS A394407: first occurrences of the totient-to-divisor-count ratio"
doi: null
url: https://oeis.org/A394407
claim: "Every prime other than 3 occurs in A394407, the positive integers whose totient-to-divisor-count ratio has no smaller positive occurrence."
strata_touched:
  - D5/S3/Arith/OeisA394407TotientTauPrimes
license: citation-only
triage: anchor

Huber’s prime conjecture for A394407

Verified locator

Source: https://oeis.org/A394407

Source statements

The unpaginated Name line reads:

Positive integers k such that there is no m < k with phi(m)/tau(m) = phi(k)/tau(k).

The unpaginated Comment line states:

Conjecture: All primes p != 3 are in the sequence; equivalently, for every prime p != 3 there is no m < p with phi(m)/tau(m) = phi(p)/tau(p) = (p - 1)/2; equivalently, the sequence is a supersequence of A045344.

Here phi is Euler’s totient and tau counts positive divisors. The variables compared by the sequence are positive integers, and the quotient is rational. The entry’s examples give phi(14)/tau(14) = 6/4 = 3/2 and the collision phi(1)/tau(1) = 1/1 = 2/2 = phi(3)/tau(3), which excludes 3.