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摘要: In the first section we study the geometric mean of exponents in the prime factorization of n!. In the second section we study the contribution of restricted primes to the sum n≤x Ω(n). Mathematics Subject Classification: 11A99, 11B99....
We define a new arithmetical function, namely, the product of the exponents in the prime factorization of an integer. We also study the product of the number of divisors of a number. Some asymptotic for-mulae are obtained and a strong connection between these arithmetical functions and the pri...
Journal of Number TheoryJ. W. Sander, On the parity of exponents in the prime factorization of factorials, J. Number Theory 90 (2001), no. 2, 316-328.Sander, J. W. (2001). On the Parity of Exponents in the Prime Factorization of Factorials. Journal of Number Theory. 90:316-328....
Let f ( n ) be the number of distinct exponents in the prime factorization of the natural number n . We prove some results about the distribution of f ( n ). In particular, for any positive integer k , we obtain thatandas x ightarrow +\\infty x ightarrow +\\infty , where \\...
Bulletin of the Iranian Mathematical Society - The aim of this paper is to study the balancing of prime factors and their exponents in the standard factorization of n! into primes. We obtain...doi:10.1007/s41980-022-00707-xHassani, Mehdi...
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