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 30
- 30 is the first sphenic number, that is the smallest number with 3 distinct prime divisors
- 30 is the largest number with the property that all smaller numbers coprime to it are prime
- Up to rotations of a cube, there are 30 different ways to put numbers 1 though 6 on a die
- Both a dodecahedron and an icosahedron have 30 edges
- There are 30 numbers with zeroless pandigital squares
Rare Properties of 30
The p-primorial is the product of all primes less than or equal to p. It is sometimes denoted by p#.
Compare to compositorials and factorials.
The number is called pronic if it is the product of two consecutive numbers.
They are twice triangular numbers.
Common Properties of 30
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.