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 159

159 is the smallest number n such that n and its prime factors, in this case 3 and 53, use the same set of digits in binary (100111111 = 11 * 110101)

Common Properties of 159

Composite

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

Composite numbers are opposite to prime numbers.

...,
155,
156,
158,
159,
160,
161,
162,
...

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.

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155,
157,
158,
159,
161,
163,
164,
...

Evil

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

Guess what odious numbers are.

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153,
154,
156,
159,
160,
163,
165,
...

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.

...,
135,
141,
151,
159,
163,
169,
171,
...

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.

...,
153,
155,
157,
159,
161,
163,
165,
...

Square-free

A number is said to be square-free if its prime decomposition contains no repeated factors.

...,
155,
157,
158,
159,
161,
163,
165,
...

Tanya Khovanova

Number Gossip

Unique Properties of 159

Common Properties of 159