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How do you show that two numbers are amicable?
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.
Are 220 and 284 amicable?
Note: 220 and 284 are examples of amicable numbers. The factors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, and 110, which sum to 284, while the factors of 284 are 1, 2, 4, 71, and 142, which sum to 220.
What is amicable number example?
…“amicable numbers”: two numbers are amicable if each is equal to the sum of the proper divisors of the other (for example, 220 and 284).
Why is 220 a special number?
In the world of numbers, 220 and 284 are special because they come as a pair. They are a pair because, if you take all the numbers that divide 220 (1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110 – but not 220 itself) and add them together you get 284.
What is a amicable number?
In mathematics: Number theory. …“amicable numbers”: two numbers are amicable if each is equal to the sum of the proper divisors of the other (for example, 220 and 284). Attributing virtues such as friendship and justice to numbers was characteristic of the Pythagoreans at all times.
Are there any pairs of amicable numbers in the world?
where n > 1 is an integer and p, q, and r are prime numbers, then 2n×p×q and 2n×r are a pair of amicable numbers. This formula gives the pairs (220, 284) for n = 2, (17296, 18416) for n = 4, and (9363584, 9437056) for n = 7, but no other such pairs are known.
When are two numbers in an array amicable?
Given an array of integers, print the number of pairs in the array that form an amicable pair. 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.
How to solve the problem of amicable pairs?
An amicable pair that exceed our search limit is considered suitable. By finding a fast way to sieve the sum of proper divisors we both solve this problem and the somewhat more challenging HackerRank version. We begin by initializing a list, ds [], to all ones, L elements long and fill it by sieving the sum of proper divisors.
Who was the first person to discover amicable numbers?
Thābit ibn Qurra’s formula was rediscovered by Fermat (1601–1665) and Descartes (1596–1650), to whom it is sometimes ascribed, and extended by Euler (1707–1783). It was extended further by Borho in 1972. Fermat and Descartes also rediscovered pairs of amicable numbers known to Arab mathematicians. Euler also discovered dozens of new pairs.