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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Further divisibility properties of the $q$-tangent numbers
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by Dominique Foata PDF
Proc. Amer. Math. Soc. 81 (1981), 143-148 Request permission

Abstract:

The $q$-tangent number ${T_{2n + 1}}(q)$ is shown to be divisible by ${(1 + q)^{a(n,1)}}{(1 + {q^2})^{a(n,2)}} \cdots {(1 + {q^n})^{a(n,n)}}$, where the $a(n,i)$’s are positive integers having the maximal property that $a(n,1) + a(n,2) + \cdots + a(n,n) = 2n$ whenever $n$ is a power of 2.
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 81 (1981), 143-148
  • MSC: Primary 05A15
  • DOI: https://doi.org/10.1090/S0002-9939-1981-0589157-8
  • MathSciNet review: 589157