220

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. 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.