odditudes-and-weirdities

Happy Powerful Numbers Day! Powerful numbers  (aka squareful numbers) are ones such that for every number dividing it that is prime or 1, the square of the divisor is also a divisor. Powerful numbers are basically a subset of the composite numbers in addition to the number 1, and contain the square numbers as a subset. Here's some of the arithmetic that determines powerful numbers. We celebrate Powerful Numbers Day today because 9 and 27 are the largest powerful numbers that form a valid date: 9/27 or September 27.

Happy Square Numbers Day! Square numbers are the numbers formed when you square a positive integer, making them a fairly easy concept to grasp. Here is the beginning of the sequence: While triangular numbers are the integers representing the number of objects needed to form equilateral triangles, square numbers similarly form squares of different sizes. They are also a subset of the powerful numbers . We celebrate today as Square Numbers Day because the 2 largest consecutive square numbers that form a date are 9 and 16: 9/16 or September 16.

Happy Composite Numbers Day! Composite numbers are sort of like the complement of the prime numbers (ignoring 1, which is neither), and each of them can be expressed as two or more prime numbers. For example, 12 = 2 X 2 X 3 (2 and 3 are primes) so it is composite, and 35 = 5 X 7 (5 and 7 are primes) so it is composite. Every positive integer greater than 1 is going to be either a prime number or a composite number. A subset of the composite numbers, the semiprime numbers , are the driving force behind  public key cryptography  Other interesting subsets of the composite numbers are the sphenic numbers and the powerful numbers . December 14 was chosen for Composite Numbers Day since they are the largest consecutive composite numbers to form a date: 12/14.