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@rwst rwst commented Jan 25, 2026

Resolves #1460.

Conjectures associated with A087719

Define $\varsigma(n)$ the smallest prime factor of $n$ (Nat.minFac). Let $a_n$ be the least
number such that the count of numbers $k \le a_n$ with $k > \varsigma(k)^n$ exceeds the count
of numbers with $k \le \varsigma(k)^n$.

The conjecture states that $a_n = 3^n + 3 \cdot 2^n + 6$ for $n \ge 1$.

References: oeis.org/A087719

Note: I'm using Claude + Opus for supervised formalization tasks. Claude has no permission to use git on my machine.

@github-actions github-actions bot added the oeis Conjectures from oeis.org label Jan 25, 2026
rwst and others added 4 commits January 26, 2026 11:10
Comment on lines +74 to +76

/-- The formula value. -/
def formula (n : ℕ) : ℕ := 3 ^ n + 3 * 2 ^ n + 6
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Suggested change
/-- The formula value. -/
def formula (n : ℕ) : ℕ := 3 ^ n + 3 * 2 ^ n + 6

This not used anywhere, right?

I think it is better to inline this

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Thanks, lgtm, only this one suggestion

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math.CO/0409509 number 46

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