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 9801

9801 is the smallest number that is 9 times its reverse

Rare Properties of 9801

Pentagonal

Pentagonal numbers are of the form n(3n - 1)/2.

Pentagonal numbers are to pentagons what triangular numbers are to triangles and square numbers are to squares.

...,
9087,
9322,
9560,
9801,
10045,
10292,
10542,
...

Square

The number n is a square if it is the square of an integer.

...,
9216,
9409,
9604,
9801,
10000,
10201,
10404,
...

Common Properties of 9801

Apocalyptic power

The number n is called an apocalyptic power if 2ⁿ contains the consecutive digits 666 (in decimal).

...,
9798,
9799,
9800,
9801,
9802,
9803,
9804,
...

Composite

A positive integer greater than 1 that is not prime is called composite.

Composite numbers are opposite to prime numbers.

...,
9798,
9799,
9800,
9801,
9802,
9804,
9805,
...

Deficient

The number n is deficient if the sum of all its positive divisors except itself is less than n.

Compare with perfect and abundant numbers.

...,
9796,
9797,
9799,
9801,
9802,
9803,
9805,
...

Evil

The number n is evil if it has an even number of 1's in its binary expansion.

Guess what odious numbers are.

...,
9795,
9797,
9798,
9801,
9802,
9804,
9807,
...

Lucky

To build the lucky number sequence, start with natural numbers. Delete every second number, leaving 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, ... . The second number remaining is 3, so delete every third number, leaving 1, 3, 7, 9, 13, 15, 19, 21, ... . The next number remaining is 7, so delete every 7th number, leaving 1, 3, 7, 9, 13, 15, 21, ... . The next number remaining is 9, so delete every ninth number, etc.

Those numbers were lucky they weren't crossed out.

...,
9787,
9789,
9795,
9801,
9807,
9811,
9813,
...

Odd

A number is odd if it is not divisible by 2.

Numbers that are not odd are even. Compare with another pair -- evil and odious numbers.

...,
9795,
9797,
9799,
9801,
9803,
9805,
9807,
...

Powerful

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.

...,
9604,
9747,
9800,
9801,
10000,
10125,
10201,
...

Tanya Khovanova

Number Gossip

Unique Properties of 9801

Rare Properties of 9801

Common Properties of 9801