Arithmetic dynamics | Number theory | Divisor function | Integer sequences
In mathematics, sociable numbers are numbers whose aliquot sums form a periodic sequence. They are generalizations of the concepts of amicable numbers and perfect numbers. The first two sociable sequences, or sociable chains, were discovered and named by the Belgian mathematician Paul Poulet in 1918. In a sociable sequence, each number is the sum of the proper divisors of the preceding number, i.e., the sum excludes the preceding number itself. For the sequence to be sociable, the sequence must be cyclic and return to its starting point. The period of the sequence, or order of the set of sociable numbers, is the number of numbers in this cycle. If the period of the sequence is 1, the number is a sociable number of order 1, or a perfect number—for example, the proper divisors of 6 are 1, 2, and 3, whose sum is again 6. A pair of amicable numbers is a set of sociable numbers of order 2. There are no known sociable numbers of order 3, and searches for them have been made up to as of 1970. It is an open question whether all numbers end up at either a sociable number or at a prime (and hence 1), or, equivalently, whether there exist numbers whose aliquot sequence never terminates, and hence grows without bound. (Wikipedia).
Tutorial - What is an imaginary number
http://www.freemathvideos.com In this video playlist you will learn everything you need to know with complex and imaginary numbers
From playlist Complex Numbers
Different Types of Numbers on the number line, lesson 1 #shorts
Watch the full playlist: https://www.youtube.com/watch?v=kcxK3_sROZA&list=PL14bv5vXK2WWuODhGbpPQA0GamV5ohOVb&index=1 Natural Numbers (N), (also called positive integers, counting numbers, or natural numbers); They are the numbers {1, 2, 3, 4, 5, …} Whole Numbers (W). This is the set of na
From playlist Celebrities Teach Math: The Number System
http://www.youtube.com/view_play_list?p=8E39E839B4C6B1DE
From playlist Common Core Standards - 6th Grade
Definition of a Critical Number with Examples
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From playlist Calculus 1 Exam 2 Playlist
Imaginary numbers are any numbers that include the imaginary number i. A mix of imaginary and real numbers gives you what’s called a complex number. The primary reason we use imaginary numbers is to give us a way to find the root (radical) of a negative number. There’s no way to use real
From playlist Popular Questions
Why Truly Sociable People Hate Parties
Our age has a high esteem for parties. Yet some of us have a particular fear of them - which we're made to feel very bad about, as if this was a sure sign of being an anti-social and unfriendly person. Far from it. As this film argues, truly sociable people tend to hate parties a lot. For
From playlist SELF
Dividing Complex Numbers Example
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From playlist Complex Numbers
Fellow Short Talks: Professor Francois Caron, Oxford University
Bio Since September 2015, Professor Francois Caron has been an Associate Professor in the department of Statistics and a tutorial Fellow at Keble College, University of Oxford. From September 2013 to August 2015, he was a Marie Curie Research Fellow in the department of Statistics at the
From playlist Short Talks
Spectra of Adjacency and Laplacian Matrices of ... by Arijit Chakrabarty
PROGRAM :UNIVERSALITY IN RANDOM STRUCTURES: INTERFACES, MATRICES, SANDPILES ORGANIZERS :Arvind Ayyer, Riddhipratim Basu and Manjunath Krishnapur DATE & TIME :14 January 2019 to 08 February 2019 VENUE :Madhava Lecture Hall, ICTS, Bangalore The primary focus of this program will be on the
From playlist Universality in random structures: Interfaces, Matrices, Sandpiles - 2019
General Chemistry 1C. Lecture 06. Acids and Bases. Pt. 3.
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From playlist Chemistry 1C: General Chemistry
The Prime Number Theorem, an introduction ← Number Theory
An introduction to the meaning and history of the prime number theorem - a fundamental result from analytic number theory. Narrated by Cissy Jones Artwork by Kim Parkhurst, Katrina de Dios and Olga Reukova Written & Produced by Michael Harrison & Kimberly Hatch Harrison ♦♦♦♦♦♦♦♦♦♦ Ways t
From playlist Number Theory
Field Induced Quantum Phase Transitions in one-Dimensional Spin...by Ramesh Chandra Nath
PROGRAM FRUSTRATED METALS AND INSULATORS (HYBRID) ORGANIZERS Federico Becca (University of Trieste, Italy), Subhro Bhattacharjee (ICTS-TIFR, India), Yasir Iqbal (IIT Madras, India), Bella Lake (Helmholtz-Zentrum Berlin für Materialien und Energie, Germany), Yogesh Singh (IISER Mohali, In
From playlist FRUSTRATED METALS AND INSULATORS (HYBRID, 2022)
What makes dogs so friendly? Study finds genetic link to super out-going people
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From playlist Dog Is Love
What is the most romantic number? | Number Hub (Ep 6) | Head Squeeze
Stand-Up mathematician Matt Parker crunches some numbers to to tell us the most romantic number. Number Hub: Stand up mathematicians reveal the mind boggling stats and figures that make up the modern world. Find out your chances of winning the EuroMillions, how many molecules of your urin
From playlist Number Hub - stats that will blow your mind
Note: Probably filmed in the Pathe studio. Titles read: "And now for GABRIEL DEE - the well known Astrologer and Psychologist in 'BIRTHDAY LUCK'" M/Ss of Miss Gabriel Dee sitting at desk, she says "Those of you born between September the 23rd and October 22nd are born under the sign
From playlist NOT SO MODERN
We can often be left feeling that there is something wrong with us if we need regularly to spend a lot of time alone. But the impulse to be alone is, in fact, a sign of taking other people very seriously - and is, therefore, a symptom of being properly, rather than superficially, sociable.
From playlist RELATIONSHIPS
What are the Types of Numbers? Real vs. Imaginary, Rational vs. Irrational
We've mentioned in passing some different ways to classify numbers, like rational, irrational, real, imaginary, integers, fractions, and more. If this is confusing, then take a look at this handy-dandy guide to the taxonomy of numbers! It turns out we can use a hierarchical scheme just lik
From playlist Algebra 1 & 2
The 3 Coolest Things Built By Birds
There are a number of bird species that construct pretty cool things - today on SciShow, we'll visit with three of them... Like SciShow? Want to help support us, and also get things to put on your walls, cover your torso and hold your liquids? Check out our awesome products over at DFTBA
From playlist Biology