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Numbers of the form k + f(k).
- Source :
-
Journal of Number Theory . Sep2024, Vol. 262, p58-85. 28p. - Publication Year :
- 2024
-
Abstract
- For a function f : N → N , let N f + (x) = { n ⩽ x : n = k + f (k) for some k }. Let τ (n) = ∑ d | n 1 be the divisor function, ω (n) = ∑ p | n 1 be the prime divisor function, and φ (n) = # { 1 ⩽ k ⩽ n : gcd (k , n) = 1 } be Euler's totient function. We show that (1) x ≪ N ω + (x) , (2) x ≪ N τ + (x) ⩽ 0.94 x , (3) x ≪ N φ + (x) ⩽ 0.93 x. [ABSTRACT FROM AUTHOR]
- Subjects :
- *PRIME numbers
Subjects
Details
- Language :
- English
- ISSN :
- 0022314X
- Volume :
- 262
- Database :
- Academic Search Index
- Journal :
- Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 177537842
- Full Text :
- https://doi.org/10.1016/j.jnt.2024.03.010