Are 1 and 2 amicable numbers?

Are 1 and 2 amicable numbers?

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.

Is 5020 and 5564 amicable numbers?

The first few amicable pairs are (220, 284), (1184, 1210), (2620, 2924) (5020, 5564), (6232, 6368), (10744, 10856), (12285, 14595), (17296, 18416), (63020, 76084). (OEIS A002025 and A002046).

What is the smallest pair of friendly number?

Amicable numbers are two different numbers related in such a way that the sum of the proper divisors of each is equal to the other number. The smallest pair of amicable numbers is (220, 284).

Is 125 a happy number?

For example, starting with 7 gives the sequence 7, 49, 97, 130, 10, 1, so 7 is a happy number. The first few happy numbers are 1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100, (OEIS A007770). These are also the numbers whose 2-recurring digital invariant sequences have period 1.

Is 80 a friendly number?

The first few friendly pairs, ordered by smallest maximum element are (6, 28), (30, 140), (80, 200), (40, 224), (12, 234), (84, 270), (66, 308), (OEIS A050972 and A050973). 45) uses the term “friendly numbers” to describe amicable pairs.

What is the smallest pair of friendly numbers?

What is an example of a friendly number?

The numbers known to be friendly are given by 6, 12, 24, 28, 30, 40, 42, 56, 60, (OEIS A074902). Friendly numbers have a positive density.

What are happy and unhappy numbers?

To find out if a number is happy, replace the number by the sum of the squares of its digits. Repeat the process until either the number equals 1 or loops endlessly in a cycle that does not include 1. When the process ends with 1 then the number is described as a happy number, otherwise, it is an unhappy number.

Is 21 a happy number?

The first few happy numbers are 1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100, (OEIS A007770). These are also the numbers whose 2-recurring digital invariant sequences have period 1.

What are the properties of an amicable number?

More specifically, we can define that amicable numbers are a pair of numbers with the property that the sum of all the proper divisors of the first number (not including itself) is exactly equal to the second number while the sum of all the proper divisors of the second number (not including itself) likewise equal to the first number.

Which is the smallest pair of amicable numbers?

The smallest pair of amicable numbers is ( 220, 284 ). They are amicable because the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, of which the sum is 284; and the proper divisors of 284 are 1, 2, 4, 71 and 142, of which the sum is 220.

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.

What are the first ten amicable numbers in the world?

The first ten amicable pairs are: (220, 284), (1184, 1210), (2620, 2924), (5020, 5564), (6232, 6368), (10744, 10856), (12285, 14595), (17296, 18416), (63020, 76084), and (66928, 66992).