# Number Gossip

(Enter a number and I'll tell you everything you wanted to know about it but were afraid to ask.)

## Unique Properties of 14

• 14 is the largest number for which there are as many composite numbers less than it as there are primes
• 14 is the lowest even n for which the equation φ(x) = n has no solution, making it the first even nontotient
• There are 14 distinct combinations of four integers such that the sum of their reciprocals is 1
• 14 is the smallest positive integer n such that n and 2n end with the same digit
• 14 is the smallest number such that the sum of factorials of its digits is a square (1! + 4! = 25 = 52)
• 14 is the largest number of distinct sets obtainable by repeatedly applying the set operations of closure and complement to a given starting subset of a topological space (submitted by Corey Cheever)
• 14 is the smallest number n such that σ(n) = σ(n+1)
• 14 is the smallest number such that it and the next number are both semiprimes (14 = 2*7 and 15 = 3*5)