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 $σ_x(n)$

Details 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 $σ_x(n)$ 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

arxiv.org/abs/0903.1743v4

Mathematics

Number Theory

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

Scientific paper

For a finite sequence of positive integers $A=\{a_j\}_{j=1}^{k},$ we prove a
recursion for divisor function $\sigma_{x}^{(A)}(n)=\sum_{d|n,\enskip d\in
A}d^x.$ 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
$\sigma_x(n)$ similar to the classic pentagonal recursion in case of $x=1.$

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