Erdős problem 313

Are there infinitely many pairs `(m, P)` where `m ≥ 2` is an integer and `P` is a set of distinct primes such that the following equation holds: $\sum_{p \in P} \frac{1}{p} = 1 - \frac{1}{m}$ ?

Sources

The source's own material, retained exactly.

5 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

313.lean

Retained formal statement2 of 5

There are at least 8 primary pseudoperfect numbers. The first eight terms of A54377 are exhibited together with their explicit prime decompositions.

FormalConjectures/ErdosProblems/313.leanErdos313.erdos_313.variants.exists_at_least_eight_primary_pseudoperfect1 lineExact file

18 ≤ {n | Erdos313.IsPrimaryPseudoperfect n}.encard

TextbookStatement only, no proof