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 840
- 840 is the smallest number divisible by 1 through 8
- 840 is the smallest number n such that σ(n) = 15φ(n)
- 840 is the smallest area of exactly three Pythagorean triangles
- 840 is the smallest number n such that nτ(n)>4prime(n)
- 840 is the smallest number n such that the multiplicative group modulo n is the direct product of 5 cyclic groups
- 840 is the smallest number that is both unitary pseudoperfect and nonunitary pseudoperfect
Common Properties of 840
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.
The number n is called an apocalyptic power if 2n contains the consecutive digits 666 (in decimal).
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.