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 504
- 504 is the smallest number n, such that σ(x) = n has exactly ten solutions, where σ(x) means the sum of the divisors
- 504 is the smallest sum of numbers in an amicable pair
- 504 is the smallest number with two pairs of divisors that multiply to the number itself and are reverses of each other (504 = 42*12 = 24*21)
- 504 is the smallest number such that the digits of σ(n) are a permutation of the digits of σ(n)-n
Common Properties of 504
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.