Abstract:
This paper deals with the problems of the upper and lower orders of growth of the ratios of the divisor functions of “adjacent” binomial coefficients, i.e., of the numbers of combinations of the form CknCkn and Ck+1nCk+1n or CknCkn and Ckn+1Ckn+1. The suprema and infima of the corresponding ratios are obtained.
Keywords:
number of divisors of binomial coefficients, sum of prime divisors.
\Bibitem{Fed13}
\by G.~V.~Fedorov
\paper On the Number of Divisors of Binomial Coefficients
\jour Mat. Zametki
\yr 2013
\vol 93
\issue 2
\pages 276--285
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\transl
\jour Math. Notes
\yr 2013
\vol 93
\issue 2
\pages 308--316
\crossref{https://doi.org/10.1134/S0001434613010331}
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Linking options:
https://www.mathnet.ru/eng/mzm10161
https://doi.org/10.4213/mzm10161
https://www.mathnet.ru/eng/mzm/v93/i2/p276
This publication is cited in the following 2 articles:
Vladimir Nikolaevich Chubarikov, Gleb Vladimirovich Fedorov, Studies in Systems, Decision and Control, 30, Continuous and Distributed Systems II, 2015, 29
Fedorov G.V., “The Upper Limit Value of the Divisor Function with Growing Dimension”, Dokl. Math., 88:2 (2013), 529–531