A primitive pseudoperfect number is a pseudoperfect number for which none of its proper divisors are pseudoperfect (Guy 1994, p. 46). The first few are 6, 20, 28, 88, 104, 272, ... (OEIS A006036). Primitive pseudoperfect numbers are also called primitive semiperfect numbers (Guy 1994, p. 46) or irreducible pseudoperfect numbers. There are infinitely many primitive pseudoperfect numbers which are not harmonic divisor numbers, and infinitely many odd primitive pseudoperfect numbers.
Benkoski and Erdős (1974) asked whether the reciprocal series
 |
converges, where 
is the set of primitive pseudoperfect
numbers. This is problem 469 in the
Erdős problems collection (Bloom 2026). Lewis
(2026) reported an affirmative proof together with a kernel-checked
Lean formalization. A second Lean development was reported by VibeMathed (2026).
The public project reports proof development with GPT-5.6
Sol Ultra and review with Claude Fable 5. As of Sep. 21, 2026, independent human
review of the manuscript and its correspondence with the Lean definitions
remained pending (Lewis 2026).
