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 144
- 144 is a dozen dozens, or one gross
- 144 is the only composite square in the Fibonacci sequence
- 144 is the smallest square such that there exists another square - 441 - with the same set of digits
- 144 is the smallest abundant Fibonacci number
- 144 is the largest sum-product integer - the integer that is equal to the sum of its digits times the product of its digits
- 144 is the smallest square perimeter of a primitive Pythagorean triangle
- 144 is the smallest number such that its fifth power is the sum of other fifth powers
Rare Properties of 144
Fibonacci numbers are numbers that form the Fibonacci sequence. The Fibonacci sequence is defined as starting with 1, 1 and then each next term is the sum of the two preceding ones.
Fibonacci numbers are very common in nature. For example, a pineapple has 8 spirals if you count one way, and 13 if you count the other way.
The k-th hungry number is the smallest number n such that 2^n contains the first k digits of the decimal expansion of pi.
They are named hungry numbers because they try to eat as much "pi" as possible.
The number n is a square if it is the square of an integer.
Common Properties of 144
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.