DIVISOR‐SUM FIBERS

DOI10.1112/S0025579317000535zbMath1410.11115arXiv1706.03120MaRDI QIDQ3176198

Paul Pollack, Lola Thompson, Carl B. Pomerance

Publication date: 19 July 2018

Published in: Mathematika (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.03120

zbMATH Keywords

sum-of-proper-divisors functionprogress on EGPSsolutions of equation and congruence involving sum-of-divisors function

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Other results on the distribution of values or the characterization of arithmetic functions (11N64)

Related Items (7)

Shifts of the prime divisor function of Alladi and Erd\H{o}s ⋮ Sums of proper divisors follow the Erdős–Kac law ⋮ Powerfree sums of proper divisors ⋮ Computers as a novel mathematical reality. III: Mersenne numbers and sums of divisors ⋮ Divisor sums representable as the sum of two squares ⋮ On near-perfect numbers ⋮ Numerical and Statistical Analysis of Aliquot Sequences

Cites Work

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• On the greatest common divisor of a number and its sum of divisors
• On the numbers of the form \(\sigma(n)-n\) und \(n-\varphi(n)\).
• Über die Häufigkeit vollkommener Zahlen
• There are infinitely many Carmichael numbers
• On the number of prime factors of values of the sum-of-proper-divisors function
• Some arithmetic properties of the sum of proper divisors and the sum of prime divisors
• The distribution of integers with a divisor in a given interval
• On the number of divisors of a natural number having the form \(p-1\)
• Some problems of Erdős on the sum-of-divisors function
• Finite connected components of the aliquot graph
• Popular values of Euler's function
• The First Function and Its Iterates
• ON CONGRUENCES OF THE FORM σ(n) ≡ a (mod n)
• On the distribution of some integers related to perfect and amicable numbers
• On the congruences $σ(n) ≡ a (mod n)$ and $n ≡ a (mod φ(n))$

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