01
The problem
A unitary divisor of n is d∣ n such that (d,n/d)=1. A number n≥ 1 is a unitary perfect number if it is the sum of its unitary divisors (aside from n itself). Are there only finite many unitary perfect numbers?
Open since2004source estimate
Last checked2026.07.26Catalog verification
02
Reward offers
Offer 01$10Paul Erdős / Combinatorics Foundation
DocumentedA solution must appear in a reputable journal, with documentation that Erdős offered the displayed amount. Claims are administered by the Combinatorics Foundation; erdosproblems.com does not pay awards.