## Monday, February 8, 2016

### Chinese New Year 2016

Today, February 8, 2016, is Chinese New Year.  Just for fun, I looked through OEIS to see what interesting facts I can find about the leap year 2016.  Here are some facts about the number 2016:

1. 2016 is the sum of the divisors of both the 42th and the 47th generalized pentagonal number.
2. 2016 = 3^3+...+9^3 is the sum of 7 positive cubes.
3. The sum of divisors of 2016 squared is a multiple of 2016.
4. The 2016th Fibonacci number is a multiple of the sum of divisors of 2016 (= 6552)
5. Both 2016 and 2016^2 has 0 as smallest digit and 6 as largest digit.
6. The product of the proper divisors of 2016 is a multiple of the sum of the proper divisors of 2016.
7. Both the number of divisors of 2016 and the number of positive integers relatively prime to 2016 that are less than or equal to 2016 are perfect squares.
8. 2016 = 63*64/2 is a triangular number, i.e, it is the sum 1+2+...+63.
9. 2016 = 6!+36^2.
10. 2016 (in base 10) is divisible by the sum of their digits in every base from 2 through to 16.