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
- 144 is the smallest three-digit number in which the sum of distinct digits of the number equals the sum of its distinct prime divisors (144 = 24*34 and 1 + 4 = 2 + 3); [Cramer] checked* 79 is the least positive integer requiring the maximum number of terms, namely 19, to be expressed as a sum of positive fourth 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.