Distribution mod p of Euler’s Totient and the Sum of Proper Divisors
نویسندگان
چکیده
We consider the distribution in residue classes modulo primes p of Euler’s totient function ϕ(n) and sum-of-proper-divisors s(n):=σ(n)−n. prove that values for n≤x are coprime to asymptotically uniformly distributed among p−1 p, 5≤p≤(logx)A (with A fixed but arbitrary). also show s(n) n composite all every p≤(logx)A. These appear be first results their kind where modulus is allowed grow substantially with x.
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 2023
ISSN: ['0026-2285', '1945-2365']
DOI: https://doi.org/10.1307/mmj/20216082