Nothing much interesting happened today. Sports day went well, all is good.
However, 185 is a key number in many ways, so I thought I’d focus on that tonight.
- 185 is an odd number
- 185 is a composite number
- 185 is a deficient number, as 43 is less than 185
- 185 is an odious number
- 185 is a square-free number
- 185 is the sum of two square numbers in two different ways: 132+ 42 and 112 + 82
- 185 is the difference of 2 square numbers: 212 – 162
Some of these will need explaining!
A composite number is a positive integer that has at least one positive divisor other than one or itself. In other words a composite number is any positive integer greater than one that is not a prime number. Basically, by definition, every integer greater than one is either a prime number or a composite number. The number one is a unit; it is neither prime nor composite.
Deficient numbers work like this: for the number 21, the divisors are 1, 3, 7 and 21, and their sum is 32. However, because 32 is less than 2 × 21, the number 21 is deficient. Its deficiency is 2 × 21 − 32 = 10.
An odious number is a non-negative number that has an odd number of 1s in its binary representation. It could also be part of the Thue-Morse sequence, shown below:
A square-free, integer is one divisible by no perfect square, except 1. For example, 10 is square-free but 18 is not, as it is divisible by 9 = 32.
185 is a good number for stats!
