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 432
- An equilateral triangle whose area and perimeter are equal, has an area (and perimeter) equal to the square root of 432
- 432 is the smallest number n such that n! is not divisible by the sum of the digits of n!
- 432 is the smallest sum of consecutive cubes that is sandwiched between twin primes
- 432 is the Achilles number whose double is also an Achilles number (Achilles numbers are powerful but not powers)
- 432 is the smallest number such that, in its prime factorization, the product of the exponents equals the sum of the prime factors and exponents
Common Properties of 432
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.
An integer n is powerful if for every prime p dividing n, p2 also divides n.
How much power? They all can be written as a2 b3.
The number n is practical if all numbers strictly less than n are sums of distinct divisors of n.