odditudes-and-weirdities

Happy Deficient Numbers Day! Deficient numbers (aka defective numbers) are the somewhat disdainful name for the natural numbers that are the companions for the more prestigiously named perfect numbers and abundant numbers . They are numbers where the sum of their divisors is less than twice that number. The start of the deficient numbers is below. It's known that there are an infinite number of both even and odd deficient numbers. Though most odd numbers are deficient, there are exceptions; 945 is the smallest odd abundant number, and thus is the first odd number that's not deficient. Here is the classification the beginning of the natural numbers into deficient, abundant, and perfect numbers. (Some are also noted as semiperfect or almost perfect numbers .) We celebrate the deficient numbers today because the highest 2 consecutive deficient numbers that can form a date are 11 and 13: 11/13 or November 13.

Happy Abundant Numbers Day! What are abundant numbers  (aka excessive numbers)? They are related to the concept of perfect numbers , which are the numbers where the sum of the proper divisors is equal to 2 times the number itself. Abundant numbers are where the sum of the proper divisors is greater than the number. (The remainder, numbers where the sum of the proper divisors is less than the number, are called deficient numbers .) Here is the start of the set of abundant numbers. Every natural number is either perfect, abundant, or deficient. Here's the arithmetic that determines some of the early ones. We celebrate Abundant Numbers Day today because 12 and 18 are the 2 largest consecutive abundant numbers that form a date: 12/18 or December 18.