Journal of Integer Sequences, Vol. 20 (2017), Article 17.5.6

On Sums of Powers of the p-adic Valuation of n!

Rafael Jakimczuk
División Matemática
Universidad Nacional de Luján
Buenos Aires


We study sums where the multiplicities of the primes in the prime factorization of n! appear, and obtain a strong connection between these sums and the Riemann zeta function.

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Received February 10 2017; revised version received April 9 2017. Published in Journal of Integer Sequences, May 1 2017.

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