220 (number) explained

220 (two hundred [and] twenty) is the natural number following 219 and preceding 221.

In mathematics

It is a composite number, with its proper divisors being 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, making it an amicable number with 284.^{[1] [2]} Every number up to 220 may be expressed as a sum of its divisors, making 220 a practical number.

It is the sum of four consecutive primes (47 + 53 + 59 + 61). It is the smallest even number with the property that when represented as a sum of two prime numbers (per Goldbach's conjecture) both of the primes must be greater than or equal to 23.There are exactly 220 different ways of partitioning 64 = 8² into a sum of square numbers.

It is a tetrahedral number, the sum of the first ten triangular numbers, and a dodecahedral number. If all of the diagonals of a regular decagon are drawn, the resulting figure will have exactly 220 regions.

It is the sum of the sums of the divisors of the first 16 positive integers.^[3]

Notes

1. Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 167
2. Book: Higgins, Peter . Number Story: From Counting to Cryptography . limited . 2008 . Copernicus . New York . 978-1-84800-000-1 . 61 .
3. sum_ sigma(k) where sigma(n) = sum of divisors of n.

References

• Wells, D. (1987). The Penguin Dictionary of Curious and Interesting Numbers (pp. 145 – 147). London: Penguin Group.