Arithmetic dynamics | Divisor function | Integer sequences
In mathematics, an almost perfect number (sometimes also called slightly defective or least deficient number) is a natural number n such that the sum of all divisors of n (the sum-of-divisors function σ(n)) is equal to 2n − 1, the sum of all proper divisors of n, s(n) = σ(n) − n, then being equal to n − 1. The only known almost perfect numbers are powers of 2 with non-negative exponents (sequence in the OEIS). Therefore the only known odd almost perfect number is 20 = 1, and the only known even almost perfect numbers are those of the form 2k for some positive number k; however, it has not been shown that all almost perfect numbers are of this form. It is known that an odd almost perfect number greater than 1 would have at least six prime factors. If m is an odd almost perfect number then m(2m − 1) is a Descartes number. Moreover if a and b are positive odd integers such that and such that 4m − a and 4m + b are both primes, then m(4m − a)(4m + b) would be an odd weird number. (Wikipedia).
Perfect Numbers and Euler's Theorem
A perfect number is a number that equals the sum of its proper factors. How can we find them?
From playlist Math Play
MATH1081 Discrete Maths: Chapter 3 Question 29
Here we show there exists a perfect number. Presented by Peter Brown of the School of Mathematics and Statistics, Faculty of Science, UNSW.
From playlist MATH1081 Discrete Mathematics
Exploring an amazing pattern that forms when we multiply numbers built only with the one digit
From playlist Number Patterns
Numbers in numerology and astrology that symbolise friendship and love.
From playlist My Maths Videos
One of the oldest unsolved math problems is studying odd perfect numbers. Have fun learning the many math approaches to this problem.
From playlist Summer of Math Exposition 2 videos
HowStuffWorks Trivia! (General Knowledge No. 9)
What is a "perfect number"? Find out in this general knowledge video quiz. And yep, answers are included.
From playlist Quizz
a problem dealing with whole number sets
From playlist Common Core Standards - 7th Grade
https://sites.google.com/site/teachshsat/ SHSAT and prime numbers
From playlist SHSAT - 8th Grade Samples
Find the Least Perfect Square That Is In the Form of An Integer with Concatenation of Its Digits
Find the Least Perfect Square That Is In the Form of An Integer with Concatenation of Its Digits The number is 13223140496 13223140496 = (36 36 36 36 36 4) ^2
From playlist Elementary Number Theory
Integral points on Markoff-type cubic surfaces - Amit Ghosh
Special Seminar Topic: Integral points on Markoff-type cubic surfaces Speaker: Amit Ghosh Affiliation: Oklahoma State University Date: December 8, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Hypergraph matchings and designs – Peter Keevash – ICM2018
Combinatorics Invited Lecture 13.10 Hypergraph matchings and designs Peter Keevash Abstract: We survey some aspects of the perfect matching problem in hypergraphs, with particular emphasis on structural characterisation of the existence problem in dense hypergraphs and the existence of d
From playlist Combinatorics
More designs - P. Keevash - Workshop 1 - CEB T1 2018
Peter Keevash (Oxford) / 01.02.2018 We generalise the existence of combinatorial designs to the setting of subset sums in lattices with coordinates indexed by labelled faces of simplicial complexes. This general framework includes the problem of decomposing hypergraphs with extra edge dat
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Seaborn Python Tutorial | Complete Seaborn Crash Course | Data Visualization in Seaborn | Kgp Talkie
Seaborn is a Python data visualization library based on matplotlib. It provides a high-level interface for drawing attractive and informative statistical graphics. Statistical analysis is a process of understanding how variables in a dataset relate to each other and how those relationships
From playlist Brief Introduction to Data Science
Theory of numbers:Introduction
This lecture is part of an online undergraduate course on the theory of numbers. This is the introductory lecture, which gives an informal survey of some of the topics to be covered in the course, such as Diophantine equations, quadratic reciprocity, and binary quadratic forms.
From playlist Theory of numbers
Introduction to number theory lecture 6. Multiplicative functions.
This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 We give some examples of multiplicative functions and show how to calculate them. As an app
From playlist Introduction to number theory (Berkeley Math 115)
The Beauty of Three - https://aperture.gg/3 Start learning everything STEM with Brilliant: https://brilliant.org/aperture Merch: https://aperture.gg/merch Stay connected with Aperture: Website: https://aperture.gg/ Instagram: https://www.instagram.com/theapertureyt/ Twitter: https://twit
From playlist Philosophy & Psychology 🧠
So it's been almost 2 years since I said the random-number-machine follow-up video was coming "soon", and it's finally time! (Combined with a fun bit of math regarding perfect shuffles in reply to a fascinating Matt Parker video) If you take a histogram of the wait times between geiger tu
From playlist Prob and Stats
Perfect Numbers and Elementary Methods in Modern Research (Josh Zelinsky) | Ep. 15
Josh Zelinsky is a number theorist and teacher at the Hopkins school in New Haven, CT. We discuss his experience as a former academic teaching high school mathematics and his research to address whether there are any odd perfect numbers, one of the oldest unsolved problems in mathematics.
From playlist Daniel Rubin Show, Full episodes
Abundant, Deficient, and Perfect Numbers ← number theory ← axioms
Integers vary wildly in how "divisible" they are. One way to measure divisibility is to add all the divisors. This leads to 3 categories of whole numbers: abundant, deficient, and perfect numbers. We show there are an infinite number of abundant and deficient numbers, and then talk abou
From playlist Number Theory
Peter Scholze - Opening lecture, Arizona Winter School 2017: Perfectoid Spaces
Slides for this talk: http://swc-alpha.math.arizona.edu/video/2017/2017ScholzeOpeningSlides.pdf Video taken from: http://swc.math.arizona.edu/aws/2017/index.html
From playlist Mathematics