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Problem #1052: A unitary divisor of $n$ is $d\mid n$ such that $(d,n/d)=1$

A unitary divisor of $n$ is $d\mid n$ such that $(d,n/d)=1$. A number $n\geq 1$ is aunitary perfect numberif it is the sum of its unitary divisors...

SOLVED $10

Problem 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 finite many unitary perfect numbers?
Categories: Number Theory

Progress

Guy [Gu04] reports that Carlitz, Erdős, and Subbarao offer \$10 for settling this question, and that Subbarao offers 10 cents for each new example.

There are no odd unitary perfect numbers. There are five known unitary perfect numbers (A002827 in the OEIS):\[6, 60, 90, 87360, 146361946186458562560000.\]This is problem B3 in Guy's collection [Gu04].

Source: erdosproblems.com/1052 | Last verified: January 19, 2026

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