Does Ten Have a Friend?

Details Does Ten Have a Friend? Does Ten Have a Friend?

2008-06-05

arxiv.org/abs/0806.1001v2

Mathematics

Number Theory

Scientific paper

Any positive integer $n$ other than 10 with abundancy index 9/5 must be a
square with at least 6 distinct prime factors, the smallest being 5. Further,
at least one of the prime factors must be congruent to 1 modulo 3 and appear
with an exponent congruent to 2 modulo 6 in the prime power factorization of
$n$.

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