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 $σ_x(n)$

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dc.creatorShevelev, Vladimir
dc.date2009-03-10
dc.date2009-03-23
dc.date.accessioned2026-07-07T12:54:44Z
dc.date.available2026-07-07T12:54:44Z
dc.descriptionFor a finite sequence of positive integers $A=\{a_j\}_{j=1}^{k},$ we prove a recursion for divisor function $σ_{x}^{(A)}(n)=\sum_{d|n,\enskip d\in A}d^x.$ 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 $x=1.$
dc.description11 pages, improvement of the text of Introduction; addition of Section 5
dc.identifierhttps://arxiv.org/abs/0903.1743
dc.identifierhttp://arxiv.org/abs/0903.1743
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/224036
dc.subjectNumber Theory
dc.subject11B37
dc.titleA 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 $σ_x(n)$
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