The Infinitude of Primitive Abundant Numbers in Arithmetic Progressions

Summary

Using Dirichlet’s theorem on arithmetic progressions, we show that if a and b are positive integers with a deficient greatest common divisor, the arithmetic progression ak + b contains infinitely many primitive abundant numbers.

MSC:

• 11A25

Acknowledgments

The author thanks Professor Cem Yalçn Y ild ir im and an anonymous referee for their significant help in improving the exposition quality of the article.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Mert Ünsal

Mert Ünsal obtained his bachelor’s degree in mathematics from Boǧaziçi University and is currently pursuing a master’s degree in mathematics at the Technical University of Munich. His interests lie in number theory and probability theory.