On the coprimality of some arithmetic functions
نویسندگان
چکیده
منابع مشابه
On the Coprimality of Some Arithmetic Functions
Let φ stand for the Euler function. Given a positive integer n, let σ(n) stand for the sum of the positive divisors of n and let τ(n) be the number of divisors of n. We obtain an asymptotic estimate for the counting function of the set {n : gcd(φ(n), τ(n)) = gcd(σ(n), τ(n)) = 1}. Moreover, setting l(n) := gcd(τ(n), τ(n+ 1)), we provide an asymptotic estimate for the size of #{n 6 x : l(n) = 1}.
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ژورنال
عنوان ژورنال: Publications de l'Institut Mathematique
سال: 2010
ISSN: 0350-1302,1820-7405
DOI: 10.2298/pim1001121d