The number theoretic omega function and summations involving the exponents of prime numbers in the factorization of factorials

DOI10.1007/s41980-022-00707-xOpenAlexW4281698347WikidataQ114217331 ScholiaQ114217331MaRDI QIDQ2682740

Mahmoud Marie, Mehdi Hassani

Publication date: 1 February 2023

Published in: Bulletin of the Iranian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s41980-022-00707-x

zbMATH Keywords

prime numberfactorialLegendre's theoremgrowth of arithmetic functionsnumber theoretic omega function

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) Factorization; primality (11A51) Rate of growth of arithmetic functions (11N56) Primes (11A41)

Uses Software

• OEIS

Cites Work

• Sur quelques applications de la ``méthode de l'hyperbole de Dirichlet à la théorie des nombres premiers
• Approximate formulas for some functions of prime numbers
• Remarks on the number of prime divisors of integers
• Factorization of factorials and a result of Hardy and Ramanujan
• A Class of Additive Arithmetical Functions
• Handbook of Number Theory I
• The Second Central Moment of Additive Functions
• A remark on the number of distinct prime divisors of integers
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