Arithmetic dynamics | Perfect numbers | Divisor function | Integer sequences
In mathematics, a k-hyperperfect number is a natural number n for which the equality n = 1 + k(σ(n) − n − 1) holds, where σ(n) is the divisor function (i.e., the sum of all positive divisors of n). A hyperperfect number is a k-hyperperfect number for some integer k. Hyperperfect numbers generalize perfect numbers, which are 1-hyperperfect. The first few numbers in the sequence of k-hyperperfect numbers are 6, 21, 28, 301, 325, 496, 697, ... (sequence in the OEIS), with the corresponding values of k being 1, 2, 1, 6, 3, 1, 12, ... (sequence in the OEIS). The first few k-hyperperfect numbers that are not perfect are 21, 301, 325, 697, 1333, ... (sequence in the OEIS). (Wikipedia).
#MegaFavNumbers What’s your Mega Favourite Number?
From playlist MegaFavNumbers
MegaFavNumbers - A number with 19729 digits
This video is about my MegaFavNumber. It has 19729 digits, and it is a power of two. [This link is now broken, and I can't find it anywhere else. :( ] See all the digits here: https://sites.google.com/site/largenumbers/home/appendix/a/numbers/265536 The OEIS sequence I mentioned: https:/
From playlist MegaFavNumbers
1,010,010,101,000,011 - #MegaFavNumbers
This is my submission to the #megafavnumbers project. My number is 1010010101000011, which is prime in bases 2, 3, 4, 5, 6 and 10. I've open-sourced my code: https://bitbucket.org/Bip901/multibase-primes Clarification: by "ignoring 1" I mean ignoring base 1, since this number cannot be fo
From playlist MegaFavNumbers
#MegaFavNumbers - 7,588,043,387,109,376 by Egi
87,109,376^2=7,588,043,387,109,376. The last 8 digits is the square root😀, it's called an automorphic number which n^2 ends with n
From playlist MegaFavNumbers
My own choice for a number over 1,000,000 is this 617 digit boy: 251959084756578934940271832400483985714292821262040320277771378360436620207075955562640185258807844069182906412495150821892985591491761845028084891200728449926873928072877767359714183472702618963750149718246911650776133798590
From playlist MegaFavNumbers
My mega favourite number (MegaFavNumbers)
About #MegaFavNumbers: https://www.youtube.com/watch?v=A7eJb8n8zAw&list=PLar4u0v66vIodqt3KSZPsYyuULD5meoAo&index=2 My number (not included in the title in case anyone wants to try the problem): 13,223,140,496 Corrections/clarifications: 0:10: No leading zeroes are allowed, and n must b
From playlist MegaFavNumbers
MegaFavNumbers: All you need to go Mega is just 3 bytes
Joining the maths #MegaFavNumbers thing just because I like it. My favourity number of over 1 million is a number I remember ever since I was a child. It is used often and well known. Watch to find out why. 16777216
From playlist MegaFavNumbers
How is i equal to square root of -1?
What is 'i'? More importantly, what is a complex number? How are complex numbers relevant to the context of other familiar numbers? Chapters: 00:00 Introduction 01:46 Logo of Reals and Rationals 02:11 Expanding real numbers 03:25 Motivation using whole (natural) numbers 06:08 Planar numb
From playlist Summer of Math Exposition 2 videos
Fun with Math: Surprises with Arithmetic and Numbers
Stephen Wolfram shows kids and adults some fun unique things you can do with math. All demonstrations powered by the Wolfram Language. Originally livestreamed at: https://twitch.tv/stephen_wolfram Follow us on our official social media channels: Twitter: https://twitter.com/WolframRese
From playlist Stephen Wolfram Livestreams
How to understand the REAL NUMBER LINE - COLLEGE ALGEBRA
In this video we talk about natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers. We also show the real number line and the inequalities less than and greater than. 00:00 Intro 00:29 Number system 04:53 Visual representation of numbers 07:37 Rea
From playlist College Algebra
This video provides a basic introduction into real numbers. It explains how to distinguish them from imaginary numbers. It also discusses the difference between rational and irrational numbers as well as integers, natural numbers, and whole numbers. Examples include repeating and non-re
From playlist New Algebra Playlist
This chemistry video tutorial answers the question - what are isotopes? Isotopes are substances that are composed of the same element but consist of different mass numbers and number of neutrons. They share the same atomic number and therefore the same number of protons. This video cont
From playlist New AP & General Chemistry Video Playlist
Pascal's wager and real numbers
My entry for 3blue1brown's contest, talking about Pascal's wager and how it leads to interesting questions about (hyper)real numbers. A big shoutout to Grant for coming up with this wonderful idea. Link to Thierry Platinis channel for more on hyperreal numbers: https://www.youtube.com/cha
From playlist Summer of Math Exposition Youtube Videos
Year 13/A2 Pure Chapter 0.1 (Subsets of Real Numbers, Representatives and Proof)
Welcome to the first video for year 13 (A2) Pure Mathematics! This video is part of a series of three that I've called Chapter 0, and is meant as a foundation for Year 13. The primary reasons for doing this are that the difficulty of Year 13 is markedly harder than Year 12 content, and al
From playlist Year 13/A2 Pure Mathematics
My favorite proof of the n choose k formula!
The binomial coefficient shows up in a lot of places, so the formula for n choose k is very important. In this video we give a cool combinatorial explanation of that formula! Challenge Problems playlist: https://www.youtube.com/playlist?list=PLug5ZIRrShJGkzGsXMYQt8bi5ImYtiEMM Subscribe t
From playlist Challenge Problems
Is the Sieve of Eratosthenese past its prime?
The Sieve of Eratosthenes is an amazing tool for teaching people about prime numbers and composite numbers but it's not without its limitations. I've tried to answer the question, 'Is there a better way of representing a sieve like this?' 0:00 Sieve of Eratosthenes In the first part of t
From playlist Summer of Math Exposition Youtube Videos
MegaFavNumbers: 1000001, my MegaFavNumber #MegaFavNumbers
To the haters: this can actually be represented by the formula ﷽ = 1 - |n| where n represents any number and ﷽ represents my personal level of joy and fulfillment (measured in "Coulombs".) Also, DON'T WORRY. The item seen at 0:35 is NOT any kind of w*apon. It's nothing but a regular railro
From playlist MegaFavNumbers
ALGEBRA & PRE-ALGEBRA REVIEW: Ch 1 (15 of 53) What Are Number Sets?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what are counting numbers, whole numbers, integers, rational and irrational numbers, real numbers, and imaginary numbers. Next video in this series can be seen at: https://youtu.be/frXUlpNq4W
From playlist Michel van Biezen: MATH TO KNOW BEFORE HIGH SCHOOL