Article ID Journal Published Year Pages File Type
4593426 Journal of Number Theory 2016 17 Pages PDF
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(log⁡log⁡n)213b(log⁡log⁡n)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.

Keywords
Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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