The Divisor Functions

2018 ◽  
pp. 68-82
Author(s):  
R. Sivaramakrishnan
Keyword(s):  
Divisor Functions

scholarly journals The Divisibility of Divisor Functions

1961 ◽  
Vol 5 (1) ◽  
pp. 35-40 ◽  
Author(s):  
R. A. Rankin
Keyword(s):  
Positive Integer ◽  
Divisor Functions ◽  
Image Position ◽  
Positive Integers

For any positive integers n and v letwhere d runs through all the positive divisors of n. For each positive integer k and real x > 1, denote by N(v, k; x) the number of positive integers n ≦ x for which σv(n) is not divisible by k. Then Watson [6] has shown that, when v is odd,as x → ∞; it is assumed here and throughout that v and k are fixed and independent of x. It follows, in particular, that σ (n) is almost always divisible by k. A brief account of the ideas used by Watson will be found in § 10.6 of Hardy's book on Ramanujan [2].

scholarly journals A PRODUCT FORMULA FOR COMBINATORIC CONVOLUTION SUMS OF ODD DIVISOR FUNCTIONS

2016 ◽  
Vol 38 (2) ◽  
pp. 243-257
Author(s):  
Kwangchul Lee ◽  
Daeyeoul Kim ◽  
Gyeong-Sig Seo
Keyword(s):  
Product Formula ◽  
Convolution Sums ◽  
Divisor Functions

Sums of higher divisor functions

2021 ◽  
Vol 220 ◽  
pp. 61-74
Author(s):  
Guangwei Hu ◽  
Guangshi Lü
Keyword(s):  
Divisor Functions

scholarly journals The Shifted Convolution of Generalized Divisor Functions

2017 ◽  
Vol 2018 (24) ◽  
pp. 7681-7724 ◽  
Author(s):  
Berke Topacogullari
Keyword(s):  
Divisor Functions
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