Special Types of Numbers

Goldbach's Conjecture

a theory that you can write every even number greater than two as the sum of two primes

triangular numbers

numbers in the sequence 1, 3, 6, 10, 15, 21, 28, etc. formula for finding the nth triangular number is: (n² + n)/2

hexagonal numbers

numbers in the sequence 1, 7, 19, 37, 61, 91, etc. formula for finding the nth hexagonal number is: n³ - (n - 1)³ or 3n² - 3n + 1

square numbers

squared numbers: 1, 4, 9, 16, 25, 36, etc.

amicable numbers

two numbers are amicable if each value is equal to the sum of the proper divisors of the other

perfect numbers

a number in which the sum of its proper divisors (numbers smaller than the number in question that divide it evenly) is equal to the number in question ex. 1 + 2 + 3 = 6

happy numbers

a number is considered happy if the sum of the squares of its digits, or the sum of the squares of the sum of its squares, is equal to one

narcissistic numbers

a number that you can write by using operations involving all the digits in the number

abundant numbers

a number where the sum of its divisors must be greater than twice the number

deficient numbers

a number where the sum of the proper divisors is less than the original number