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 2022
- 2022 is the smallest number n such that n, n+1, n+2, and n+3 have the maximal exponents in prime factorization equal 1, 2, 3, and 4 correspondingly
- 2022 is the number of unimodular 3 by 3 matrices with entries in the set 0, 1, and 2
Common Properties of 2022
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.
A number is said to be square-free if its prime decomposition contains no repeated factors.
The untouchable numbers are those that are not the sum of the proper divisors of any number.