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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On primes $ p$ with $ \sigma(p\sp \alpha)=m\sp 2$


Authors: J. Chidambaraswamy and P. V. Krishnaiah
Journal: Proc. Amer. Math. Soc. 101 (1987), 625-628
MSC: Primary 11A25; Secondary 11D41
DOI: https://doi.org/10.1090/S0002-9939-1987-0911021-8
MathSciNet review: 911021
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Abstract: A. Takaku proved that for odd $ \alpha \geqslant 3,\sigma ({p^\alpha }) = {m^2},p$ being a prime, implies that $ p < {2^{{2^{\alpha + 1}}}}$. In this paper we extend this result to include almost all even integers $ \alpha $.


References [Enhancements On Off] (What's this?)

  • [1] A. Takaku, Prime numbers such that the sums of the divisors of their powers are perfect squares, Colloq. Math. 49 (1984), no. 1, 117–121. MR 774858

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DOI: https://doi.org/10.1090/S0002-9939-1987-0911021-8
Article copyright: © Copyright 1987 American Mathematical Society