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Amicable pairs with few distinct prime factors

Florian Luca

School of Mathematics, University of the Witwatersrand, Private Bag X3, Wits 2050, Johannesburg, South Africa

E-mail Address: [email protected]

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and

M. Tip Phaovibul

School of Mathematics, University of the Witwatersrand, Private Bag X3, Wits 2050, Johannesburg, South Africa

E-mail Address: [email protected]

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https://doi.org/10.1142/S1793042116501050Cited by:1 (Source: Crossref)

Abstract

An amicable pair $(m, n)$ is a pair of distinct positive integers $m, n$ such that $σ (m) = σ (n) = m + n$ , where $σ$ is the sum of divisors function. In this note, we prove that if $m < n$ are amicable and $m$ is odd, then $ω (m n) \geq 4$ , where $ω$ is the number of distinct prime factors.

Keywords:

Amicable pair

AMSC: 11F30, 11F67

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