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Amicable Numbers (Math Lair)
Amicable Numbers - Basic-mathematics .com
PDF Euler's Amicable Numbers
Perfect, amicable and sociable numbers
Amicable Numbers
Pairs of Amicable Numbers - GeeksforGeeks
Amicable numbers - Encyclopedia of Mathematics
Amicable Numbers: A Brief Introduction and Its Fascinating . . .
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The two numbers 2 n × a × b and 2 n × c will be amicable . Such pairs of numbers are called Thabit pairs . For n = 2, the pair is 220 and 284 . For n = 4, the formula gives 17,296 and 18,416 .
Amicable numbers Two numbers are said to be amicable if each number is the sum of the proper divisors of the other . A proper divisor of a number is any divisor of the number except the number itself . For example, the proper divisor of 12 are 1, 2, 3, 4, and 6 .
Euler's Amicable Numbers William Dunham Muhlenberg College "By finding so clever a recipe to generate amicable pairs, Euler provided another indication—if another were needed—of why he is so esteemed in the world of mathematics ." Dunham 10/17/07 9:30 PM Page 5
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An amicable pair is a cycle of length 2 of s, i .e ., a pair of numbers each of which equals the sum of the other's aliquot parts; the members of amicable pairs are also called amicable . The smallest such pair is (220,284) . It is conjectured that there are infinitely many amicable pairs, although, as for perfect numbers, this is not known .
Amicable Numbers is an independent research project that uses Internet-connected computers to find new amicable pairs . You can contribute to our research by running a free program on your computer . Current goal of the project is to find all amicable pairs with smallest member < 10 20 . All new findings are published regularly on the Amicable . . .
Two numbers are amicable if the first is equal to the sum of divisors of the second, and if the second number is equal to the sum of divisors of the first .
A pair of natural numbers each one of which is equal to the sum of the aliquot divisors of the other, i .e . of the divisors other than the number itself . This definition is found already in Euclid's Elements and in the works of Plato .
The first pair of amicable numbers is (220, 284) those discovered by Pythagoreans . Let us check the two numbers 220 and 284 . Proper divisors of 220 are: 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110 . Adding all the divisors of 220 we get,
I am trying to write a shell script which will find amicable numbers for given numbers which are entered by user . If found it will print the amicable no else will print "No" . I am getting the expected output but it is taking some time . It will be very helpful if code is optimize . I am running the code on git bash .
These are called Amicable Numbers, and in ancient times these numbers represented mutual harmony, perfect friendship and love . The heart parts of the keyrings are 50mm tall, 3mm thick and fit together like a jigsaw puzzle . The pack comes with two information sheets about the history and maths of Amicable Numbers .
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