Erdős Problem #1052

- $10

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?

#1052: [Gu04]

number theory

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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].

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This page was last edited 28 September 2025.

External data from the database - you can help update this
Formalised statement? Yes
Related OEIS sequences: A002827

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Additional thanks to: Boris Alexeev

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