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 96
- 96 is the smallest untouchable number such that its Euler's totient function is the same as its successor's
- 96 is the smallest number that can be written as the difference of 2 positive squares in 4 ways: 96 = 252 − 232 = 142 − 102 = 112 − 52 = 102 − 22
- 96 is the smallest integer n for which the number of primes less than or equal to n equals n/4
Common Properties of 96
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.
The untouchable numbers are those that are not the sum of the proper divisors of any number.