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 529

529 is the smallest square n such that the next prime of the square root is a substring of n (Square root of 529 is 23 and the next prime if 29)

Rare Properties of 529

Square

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

...,
400,
441,
484,
529,
576,
625,
676,
...

Common Properties of 529

Apocalyptic power

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

...,
506,
508,
528,
529,
539,
540,
541,
...

Composite

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

Composite numbers are opposite to prime numbers.

...,
526,
527,
528,
529,
530,
531,
532,
...

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.

...,
525,
526,
527,
529,
530,
531,
533,
...

Lazy caterer

The n-th lazy caterer number is the maximum number of pieces a (circular) pizza can be cut into with n (straight-line) cuts.

Unlike the situation with cake, everybody gets the toppings.

...,
436,
466,
497,
529,
562,
596,
631,
...

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.

...,
511,
517,
519,
529,
535,
537,
541,
...

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.

...,
523,
525,
527,
529,
531,
533,
535,
...

Odious

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

Guess what evil numbers are.

...,
522,
524,
527,
529,
530,
532,
535,
...

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.

...,
484,
500,
512,
529,
576,
625,
648,
...

Tanya Khovanova

Number Gossip

Unique Properties of 529

Rare Properties of 529

Common Properties of 529