## Tuesday, 19 February 2013

### TUESDAY, 19 FEBRUARY 2013

Today is the $50^{th}$ day of the year.

$50$ is an odious number and a Harshad or Niven number.

An odious number is any number that has an odd number of ones in its binary expansion.
$50_{10} = 110010_{2}$ so it has three ones in its binary form and is therefore odious.
The first 31 odious numbers are:
1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59, 61

Those numbers that are not odious are Evil Numbers.
The first 30 Evil Numbers are:
0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58

A Harshad or Niven Number is any number that is divisible by the sum of its digits.
The sum of the digits of $50$ is $5 + 0 = 5$ and, clearly, $50$ is divisible by $5$.
The first 30 Harshad numbers are:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, 45, 48, 50, 54, 60, 63, 70, 72, 80, 81