Binary representation of primes that divide a number, in decimal

formal-conjectures · oeis · ams-11

The value $a(n)$ is given by
$$ a(n) = \sum_{p \mid n, p \text{ prime}} 2^{\pi(p) - 1} $$
where $\pi(p) = \mathrm{primeCounting}(p)$ gives the 1-based index of the prime $p$.

Starting at any $n$ and iterating the map $n \mapsto a(n)$, we will always reach $0$.
- _Antti Karttunen_, Jun 18,20 2017

Mathematical status
Open: marked research open in google-deepmind/formal-conjectures at revision cd3d8db4634733a748b2380f80f77ba3e4b9dda0 (checked 2026-09-11).

Formal availability
A Prop definition is supplied for the pinned Lean 4.33.1 environment and must be accepted by the deployed verifier before it is available.

Sources and provenance
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://oeis.org/A087207
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/87207.lean
Local target: Corpus.OEIS87207.conjecture
Source SHA-256: ffb10b0c11e474b97d943171b87aa8ebacf32852c415a828a82dbfd093b15b17
Lean v4.33.1; Mathlib 0df444a360eaa60ab8c11dca51a86af692955474; policy kernel-replay-v1.
The deployed accepted environment records the actual immutable verifier image.

Research discussions are not verified proofs. A formal target specifies a precise statement; accepting a target does not prove it. Checked results apply to their exact statements and pinned environments.

Public JSON record