Journal of Integer Sequences, Vol. 27 (2024), Article 24.5.1

On Sums of Practical Numbers and Polygonal Numbers


Sai Teja Somu
JustAnswer
Bengaluru 560052
India

Duc Van Khanh Tran
Department of Mathematics
University of Texas at Austin
Austin, TX 78712
USA

Abstract:

Practical numbers are positive integers n such that every positive integer less than or equal to n can be written as a sum of distinct positive divisors of n. We show that all positive integers can be written as a sum of a practical number and a triangular number, resolving a conjecture by Sun. We also show that all sufficiently large natural numbers can be written as a sum of a practical number and two s-gonal numbers.


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(Concerned with sequences A000217 A005153 A208244.)


Received March 17 2024; revised versions received April 25 2024; April 30 2024. Published in Journal of Integer Sequences, May 1 2024.


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