Determining all Biunitary Triperfect Numbers of a Certain Form
Tomohiro Yamada
Center for Japanese Language and Culture
Osaka University
562-8678, 3-5-10, Sembahigashi
Minoo, Osaka
Japan
Abstract:
A divisor d of an integer N is called a unitary divisor of N if d and N/d are relatively prime
and a biunitary divisor of N if d and N/d have no common unitary divisor except 1.
An integer N is called a biunitary triperfect number if the
sum σ**(N) of biunitary divisors of N
is equal to 3N.
We show that 2160 is the only biunitary triperfect number divisible by
27 = 33.
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(Concerned with sequences
A000396
A005820
A038843
A188999
A189000
A318175
A318781.)
Received June 27 2025; revised version received August 6 2025.
Published in Journal of Integer Sequences,
August 6 2025.
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