Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4593426 | Journal of Number Theory | 2016 | 17 Pages |
Abstract
Let q≥2q≥2 be an integer and Sq(n)Sq(n) denote the sum of the digits in base q of the positive integer n. It is proved that for every real number α and β with α<βα<β,limx⟶+∞1x♯{n≤x:α≤v(φ(n))−12b(loglogn)213b(loglogn)32≤β}=12π∫αβe−t22dt, where v(n)v(n) is either ω˜(n) or Ω˜(n), the number of distinct prime factors and the total number of prime factors p of a positive integer n such that Sq(p)≡amodb (a,b∈Za,b∈Z, b≥2b≥2). This extends the results known through the work of P. Erdős and C. Pomerance, M.R. Murty and V.K. Murty to primes under digital constraint.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
M. Mkaouar, W. Wannes,