Problem 1052

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Statement. A unitary divisor of $n$ is $d\mid n$ such that $(d,n/d)=1$. A number $n\geq 1$ is a unitary perfect number if it is the sum of its unitary divisors (aside from $n$ itself).

Are there only finitely many unitary perfect numbers?

Status. Open.

Source. erdosproblems.com/1052, accessed 2026-09-04. Cite as: T. F. Bloom, Erdős Problem #1052, https://www.erdosproblems.com/1052.

References.

• [Gu04] Guy, Richard K., Unsolved problems in number theory. Third edition, Problem Books in Mathematics, Springer, New York (2004), xviii+437 pp.; doi:10.1007/978-0-387-26677-0. Section B3 "Unitary perfect numbers", p. 84, records Subbarao's conjecture of finitely many even unitary perfect numbers, the prize offers of Subbarao, Carlitz and Erdős, and the four small examples. Library home: guy_2004_unsolved_problems_number_theory.

Formalization. Statement in formal-conjectures.

Progress

Not yet compiled.

Known Results

Not yet compiled.

Linked library material

These entries are derived from explicit links on library pages. They are navigation only and do not by themselves record mathematical progress.

• maciejewski_2026_bounded_box_reductions_subbarao_warren_problem
• guy_2004_unsolved_problems_number_theory