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 84
- 84 is the smallest number that can be expressed as the sum of 3 distinct primes raised to distinct prime exponents: 84 = 25 + 33 + 52
- 84 is the smallest area of integer-sided triangle whose area equals twice its perimeter
- 84 is the smallest multidigit (and the only 2-digit) number n such that the sum of digits of n equals the sum of prime divisors of n
Rare Properties of 84
A tetrahedral number is the number of balls you can put in a triangular pyramid.
This is the space generalization of triangular and square numbers.
Common Properties of 84
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 odious if it has an odd number of 1's in its binary expansion.
Guess what evil numbers are.
The number n is practical if all numbers strictly less than n are sums of distinct divisors of n.