Number Theory

On the Almost Perfect Number Conjecture Structure and Explicit Bounds for Odd Solutions, with a Lean 4 Formalisation

Authors: Ibrahim Amin Nicola Shnoudi

A positive integer n is almost perfect if σ(n) = 2n − 1. Every power of 2 is almost perfect, and the conjecture that there are no others is open. This project does not prove it. It proves the conjecture for odd parts with at most two prime factors, with a machine-checked proof, and it reduces each remaining case to a precisely stated problem.

Comments: 18 Pages.

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Submission history

[v1] 2026-10-31 21:56:00

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