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 462
- 462 is the smallest product of four different primes sandwiched between twin primes (submitted by Massimo Kofler)
- Assuming the Generalized Riemann Hypothesis, 462 is the largest number that is not of the form ab + bc + ca for positive integers a, b, and c
Rare Properties of 462
The number is called pronic if it is the product of two consecutive numbers.
They are twice triangular numbers.
Common Properties of 462
The number n is abundant if the sum of all its positive divisors except itself is more than n.
They are abundant above perfection, not to mention deficiency. See perfect and deficient numbers.
A positive integer greater than 1 that is not prime is called composite.
Composite numbers are opposite to prime 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 number n is practical if all numbers strictly less than n are sums of distinct divisors of n.
A number is said to be square-free if its prime decomposition contains no repeated factors.