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April 2021 An identity for the sum of inverses of odd divisors of n in terms of the number of representations of n as a sum of squares
Sumit Kumar Jha
Rocky Mountain J. Math. 51(2): 581-583 (April 2021). DOI: 10.1216/rmj.2021.51.581

Abstract

Let cr(n) be the number of representations of a positive integer n as a sum of r squares, where representations with different orders and different signs are counted as distinct. We prove a combinatorial identity relating this quantity to the sum of inverses of odd divisors of n:

oddd|n1d=12r=1n(1)n+rrnrcr(n).

Citation

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Sumit Kumar Jha. "An identity for the sum of inverses of odd divisors of n in terms of the number of representations of n as a sum of squares." Rocky Mountain J. Math. 51 (2) 581 - 583, April 2021. https://doi.org/10.1216/rmj.2021.51.581

Information

Received: 5 July 2020; Revised: 23 October 2020; Accepted: 23 October 2020; Published: April 2021
First available in Project Euclid: 25 June 2021

Digital Object Identifier: 10.1216/rmj.2021.51.581

Subjects:
Primary: 11A05 , 11P99

Keywords: Faà di Bruno's formula , Jacobi's theta function , partial Bell polynomials , sum of divisors , sum of squares

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.51 • No. 2 • April 2021
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