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 46
- 46 is the number of human chromosomes
- 46 is the least even number 2k such that the sum of the first k primes is divisible by 2k
- The Tutte graph has 46 vertices
- 46 is the largest even integer for which there is no pair of abundant numbers that add up to it
Common Properties of 46
A positive integer greater than 1 that is not prime is called composite.
Composite numbers are opposite to prime numbers.
The number n is deficient if the sum of all its positive divisors except itself is less than n.
Compare with perfect and abundant numbers.
A number is even if it is divisible by 2.
Numbers that are not even are odd. Compare with another pair -- evil and odious numbers.
The number n is evil if it has an even number of 1's in its binary expansion.
Guess what odious numbers are.
The n-th lazy caterer number is the maximum number of pieces a (circular) pizza can be cut into with n (straight-line) cuts.
Unlike the situation with cake, everybody gets the toppings.
A number is said to be square-free if its prime decomposition contains no repeated factors.