English

Does Ten Have a Friend?

Number Theory 2008-06-06 v2 General Mathematics

Abstract

Any positive integer nn 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 nn.

Keywords

Cite

@article{arxiv.0806.1001,
  title  = {Does Ten Have a Friend?},
  author = {Jeffrey Ward},
  journal= {arXiv preprint arXiv:0806.1001},
  year   = {2008}
}
R2 v1 2026-06-21T10:47:53.027Z