Number Gossip

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Unique Properties of 4095

4095 is the largest triangular number of the form 2^k - 1

Common Properties of 4095

Abundant

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.

...,
4086,
4088,
4092,
4095,
4098,
4100,
4104,
...

Composite

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

Composite numbers are opposite to prime numbers.

...,
4090,
4092,
4094,
4095,
4096,
4097,
4098,
...

Evil

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

Guess what odious numbers are.

...,
4089,
4090,
4092,
4095,
4097,
4098,
4100,
...

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.

...,
4063,
4069,
4081,
4095,
4105,
4107,
4129,
...

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.

...,
4089,
4091,
4093,
4095,
4097,
4099,
4101,
...

Triangular

If you start with n points on a line, then draw n-1 points above and between, then n-2 above and between them, and so on, you will get a triangle of points. The number of points in this triangle is a triangle number.

Compare to square, pentagonal and tetrahedral numbers.

...,
3828,
3916,
4005,
4095,
4186,
4278,
4371,
...

Tanya Khovanova

Number Gossip

Unique Properties of 4095

Common Properties of 4095