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 Almost Perfect Numbers Day! Today we celebrate numbers that aren't perfect numbers but are almost perfect numbers  (aka slightly deficient numbers aka least defective numbers). Perfect numbers (in case you've forgotten) are the numbers such that if you sum up their divisors the result is 2 times the number itself. For example, the divisors of 6 are 1, 2, 3, and 6, and if you sum them up you get 1+2+3+6=12, which is also 2 x 6. Almost perfect numbers are numbers where the sum of the divisors is 1 less than 2 times the number. For example, the divisors of 4 are 1, 2, and 4, and the sum of them is 1+2+4 = 7, which is 1 less than 2 x 4. All the known almost perfect numbers are powers of 2, like 2x2 = 4, 2x2x2 = 8, 2x2x2x2 = 16, etc. It hasn't been proven that every almost perfect number is of this form, though given the computational power we have today, if other forms exist, they must be very large almost perfect numbers. Here is the beginning of the almost perfect numb...