Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

An upper bound of $\sum 1/(a_ i\log a_ i)$ for primitive sequences
HTML articles powered by AMS MathViewer

by David A. Clark PDF
Proc. Amer. Math. Soc. 123 (1995), 363-365 Request permission

Abstract:

A sequence $A = \{ {a_i}\}$ of positive integers is called primitive if no term of the sequence divides any other. Erdös conjectures that, for any primitive sequence A, \[ \sum \limits _{a \leq n,a \in A} {\frac {1}{{a\log a}} \leq \sum \limits _{p \leq n} {\frac {1}{{p\log p}},\quad {\text {for}}\;n > 1,} } \] where the sum is over all primes less than or equal to n. We show that \[ \sum \limits _{a \in A} {\frac {1}{{a\log a}} \leq {e^\gamma } < 1.7811,} \] where $\gamma$ is Euler’s constant.
References
    P. Erdös and Z. Zhang, Upper bound of $\sum {1/({a_i}\log {a_i})}$ for primitive sequences, Proc. Amer. Math. Soc. 117 (1993), 891-895.
  • J. Barkley Rosser and Lowell Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math. 6 (1962), 64–94. MR 137689
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 11B83
  • Retrieve articles in all journals with MSC: 11B83
Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 363-365
  • MSC: Primary 11B83
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1243164-0
  • MathSciNet review: 1243164