Sums of the divisor and unitary divisor functions.

1978 ◽  
Vol 1978 (302) ◽  
pp. 1-15 ◽  
Keyword(s):  
Divisor Functions ◽  
Unitary Divisor

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

The Fifth Unitary Perfect Number

1975 ◽  
Vol 18 (1) ◽  
pp. 115-122 ◽  
Author(s):  
Charles R. Wall
Keyword(s):  
Positive Integer ◽  
Perfect Number ◽  
Unitary Divisor ◽  
Perfect Numbers ◽  
Image Position

A divisor d of a positive integer n is a unitary divisor if d and n/d are relatively prime. An integer is said to be unitary perfect if it equals the sum of its proper unitary divisors. Subbarao and Warren [2] gave the first four unitary perfect numbers: 6, 60, 90 and 87360. In 1969,1 reported [3] thatis also unitary perfect. The purpose of this paper is to show that this last number, which for brevity we denote by W, is indeed the next unitary perfect number after 87360.

Sums of higher divisor functions

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

Export Citation Format

Share Document