Number Gossip

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Unique Properties of 631

631 is the smallest prime formed by reverse concatenation of three consecutive triangular numbers

Common Properties of 631

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.

...,
627,
628,
629,
631,
632,
633,
634,
...

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.

...,
529,
562,
596,
631,
667,
704,
742,
...

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.

...,
615,
619,
621,
631,
639,
643,
645,
...

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.

...,
625,
627,
629,
631,
633,
635,
637,
...

Odious

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

Guess what evil numbers are.

...,
625,
626,
628,
631,
632,
635,
637,
...

Prime

A prime is a positive integer greater than 1 that is divisible by no positive integers other than 1 and itself.

Prime numbers are opposite to composite numbers.

...,
613,
617,
619,
631,
641,
643,
647,
...

Square-free

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

...,
626,
627,
629,
631,
633,
634,
635,
...

Tanya Khovanova

Number Gossip

Unique Properties of 631

Common Properties of 631