Divisor function | Integer sequences
In mathematics, a superabundant number (sometimes abbreviated as SA) is a certain kind of natural number. A natural number n is called superabundant precisely when, for all m < n where σ denotes the sum-of-divisors function (i.e., the sum of all positive divisors of n, including n itself). The first few superabundant numbers are 1, 2, 4, 6, 12, 24, 36, 48, 60, 120, ... (sequence in the OEIS). For example, the number 5 is not a superabundant number because for 1, 2, 3, 4, and 5, the sigma is 1, 3, 4, 7, 6, and 7/4 > 6/5. Superabundant numbers were defined by Leonidas Alaoglu and Paul Erdős. Unknown to Alaoglu and Erdős, about 30 pages of Ramanujan's 1915 paper "Highly Composite Numbers" were suppressed. Those pages were finally published in The Ramanujan Journal 1 (1997), 119–153. In section 59 of that paper, Ramanujan defines generalized highly composite numbers, which include the superabundant numbers. (Wikipedia).
#MegaFavNumbers What’s your Mega Favourite Number?
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11. Marxian Exploitation and Distributive Justice
Moral Foundations of Politics (PLSC 118) Exploitation is an important technical--not normative--concept in the theory of Karl Marx. Although we are dealing with voluntary Pareto transactions, under capitalism, exploitation occurs whether or not an individual is better off. Capitalism is
From playlist The Moral Foundations of Politics with Ian Shapiro
19861: A Superabundant Odyssey - #MegaFavNumbers
A tale of superabundant numbers, the Riemann Hypothesis, and a proof by assumption. This video is part of the #MegaFavNumbers collaboration: https://www.youtube.com/playlist?list=PLar4u0v66vIodqt3KSZPsYyuULD5meoAo Special thanks to Dr. Jonathan Clark and Dr. Ben Braun for their roles in
From playlist MegaFavNumbers
12. The Marxian Failure and Legacy
Moral Foundations of Politics (PLSC 118) We previously established that the reality of scarcity invalidates Marx's core idea of superabundance, and mortally wounds his theory. Certainly, his historical predictions about worker-led socialist revolutions around the world were off-mark. To
From playlist The Moral Foundations of Politics with Ian Shapiro
16. The Rawlsian Social Contract
Moral Foundations of Politics (PLSC 118) The next and final Enlightenment tradition to be examined in the class is that of John Rawls, who, according to Professor Shapiro, was a hugely important figure not only in contemporary political philosophy, but also in the field of philosophy as
From playlist The Moral Foundations of Politics with Ian Shapiro
Normally when we think of metabolism, we think of weight loss fads like the Keto diet, the Paleo diet or intermittent fasting. Metabolism, however, is way more interesting than weight loss trends. It is the process used by your body to transform Cap'n Crunch into brain cells, and some scie
From playlist The Origin of Life
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
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Colloque d'histoire des sciences "Gaston Darboux (1842 - 1917)" - Hélène Gispert - 17/11/17
En partenariat avec le séminaire d’histoire des mathématiques de l’IHP Darboux c’est aussi le nom d’un journal : le Bulletin des sciences mathématiques (1869-1917) Hélène Gispert, GHDSO, Université Paris-Sud 11 À l’occasion du centenaire de la mort de Gaston Darboux, l’Institut Henri Poi
From playlist Colloque d'histoire des sciences "Gaston Darboux (1842 - 1917)" - 17/11/2017
25. Democratic Justice: Applications
Moral Foundations of Politics (PLSC 118) Professor Shapiro guides the class through some practical applications of his theory of democratic justice. As applied to governing children, a sphere in which power-based hierarchy is inevitable, he circumscribes the role of the state as the fid
From playlist The Moral Foundations of Politics with Ian Shapiro
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:/
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How much time you'd need to find if this giant number is a prime or composite? | MegaFavNumbers
9999999999999999999999999999999991 is the hero of our video. And how a high school piece of knowledge can help find if this particular 34 digit number is prime or not, in a very short time! The beauty of math lies in its simplicity and seemingly unexpected connections among itself. #Mega
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Conversion Arcs and 2,916,485,648,612,232,232,816 (MegaFavNumbers)
I'm sorry. The MegaFavNumbers playlist: https://www.youtube.com/playlist?list=PLar4u0v66vIodqt3KSZPsYyuULD5meoAo
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MegaFavNumbers | 8.07x10^67 vs. 137,327,459,106,673,000,000,000,000,000,000,000,000,000,000,000,000
This video compares the number of ways to shuffle a deck of cards to the number of atoms on Earth. #MegaFavNumbers 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000 vs 137,327,459,106,673,000,000,000,000,000,000,000,000,000,000,000,000.00
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MegaFavNumbers: Plus One Primes, 154,641,337, and 62,784,382,823
My entry in the #MegaFavNumbers series looks at a particularly striking example of a very specific family of primes -- and how it connects to what digits can be the final digit of primes in different bases.
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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
#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
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