A combinatorial proof of a recurrence relation for the sum of divisors function

Sun Kim

doi:10.1142/S1793042120400084

A combinatorial proof of a recurrence relation for the sum of divisors function

Sun Kim^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

Abstract

We give a combinatorial proof of a generalization of an identity involving the sum of divisors function σ(n) and the partition function p(n), which is a companion of Euler's recurrence formula for σ(n).

Original language	English
Pages (from-to)	647-653
Number of pages	7
Journal	International Journal of Number Theory
Volume	17
Issue number	3
DOIs	https://doi.org/10.1142/S1793042120400084
State	Published - 2021.04

Keywords

Euler's pentagonal number theorem
Euler's recurrence formula
sum of the divisors function
theta functions

Quacquarelli Symonds(QS) Subject Topics

Mathematics

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10.1142/S1793042120400084

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title = "A combinatorial proof of a recurrence relation for the sum of divisors function",

abstract = "We give a combinatorial proof of a generalization of an identity involving the sum of divisors function σ(n) and the partition function p(n), which is a companion of Euler's recurrence formula for σ(n).",

keywords = "Euler's pentagonal number theorem, Euler's recurrence formula, sum of the divisors function, theta functions",

author = "Sun Kim",

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year = "2021",

month = apr,

doi = "10.1142/S1793042120400084",

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AB - We give a combinatorial proof of a generalization of an identity involving the sum of divisors function σ(n) and the partition function p(n), which is a companion of Euler's recurrence formula for σ(n).

KW - Euler's pentagonal number theorem

KW - Euler's recurrence formula

KW - sum of the divisors function

KW - theta functions

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A combinatorial proof of a recurrence relation for the sum of divisors function

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

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