Perfect number, a positive integer that is equal to the sum of its proper divisors. The smallest perfect number is 6, which is the sum of 1, 2, and 3. Other perfect numbers are 28, 496, and 8,128.

The primes are a good example. After noticing the primes then one can show the prime factorization theorem. Primes can be used to design a cryptographical system (RSA) powerful enough to protect many financial transactions at the current time. Perfect numbers create a “playground” for the interested.

amicable if each of them is the sum of all proper divisors of the other. they are called perfect numbers, otherwise they form an amicable pair. The first perfect numbers 6, 28, 496, 8128, and the smallest amicable pair 220, 284, were known to the Greek mathematicians.

…“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.

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.

91 = 63 + (-5)3 = 43 + 3. Numbers that are the smallest number that can be expressed as the sum of two cubes in n distinct ways have been dubbed “taxicab numbers”….1729 (number)

three numbers

Pythagoras

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.