Journal of Integer Sequences, Vol. 26 (2023), Article 23.2.5

Sums of Squares, Triangular Numbers, and Divisor Sums


G. E. Andrews
Department of Mathematics
Pennsylvania State University
University Park, PA 16802
USA

Sumit Kumar Jha
310, CS-Luxurio
Gachibowli
Hyderabad
India

J. López-Bonilla
ESIME-Zacatenco
Instituto Politécnico Nacional
Edif. 4, 1er. Piso
Col. Lindavista
07738 Ciudad de México
Mexico

Abstract:

We prove a general theorem that can be used to derive recurrences for familiar arithmetic functions such as rk(n) and tk(n), the number of representations of n as a sum of k squares and k triangular numbers, respectively.

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(Concerned with sequences A000041 A000118.)

Received October 15 2022; revised versions received October 16 2022; February 9 2023; February 12 2023; February 25 2023. Published in Journal of Integer Sequences, February 25 2023.

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