Geodesic
On sums of powers of the \(p\)-adic valuation of \(n!\)
Journal of integer sequences, Tome 20 (2017) no. 5
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.
Keywords: factorial, prime factorization, Riemann zeta function 
@article{JIS_2017__20_5_a5,
     author = {Jakimczuk,  Rafael},
     title = {On sums of powers of the \(p\)-adic valuation of \(n!\)},
     journal = {Journal of integer sequences},
     year = {2017},
     volume = {20},
     number = {5},
     zbl = {1405.11128},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2017__20_5_a5/}
}
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Jakimczuk,  Rafael. On sums of powers of the \(p\)-adic valuation of \(n!\). Journal of integer sequences, Tome 20 (2017) no. 5. http://geodesic.mathdoc.fr/item/JIS_2017__20_5_a5/