A recursion for divisor function over divisors belonging to a prescribed finite sequence of positive integers and a solution of the Lahiri problem for divisor function σ_x(n)

2009/03/10 by Vladimir Shevelev, Shevelev, Vladimir
Computer Science · Mathematics · #Advanced Mathematical Theories #Analytic Number Theory Research #Coding theory and cryptography #math.NT #msc:11B37

paper · pdf · doi:10.48550/arxiv.0903.1743

11 pages, improvement of the text of Introduction; addition of Section 5

arxiv created 2009/03/23 · arxiv updated 2009/12/01

Abstract

For a finite sequence of positive integers A=\a_j\_j=1^k, we prove a recursion for divisor function σ_x^(A)(n)=∑_{d|n,\enskip d∈ A}d^x. As a corollary, we give an affirmative solution of the problem posed in 1969 by D. B. Lahiri [3]: to find an identity for divisor function σ_x(n) similar to the classic pentagonal recursion in case of x=1.

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