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 673

673 is the smallest prime which is one greater than a triperfect number
673 is the smallest prime whose base-4 representation is a square when read in base 10

Common Properties of 673

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.

...,
669,
670,
671,
673,
674,
675,
676,
...

Evil

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

Guess what odious numbers are.

...,
667,
669,
670,
673,
674,
676,
679,
...

Happy

One can take the sum of the squares of the digits of a number. Those numbers are happy for which iterating this operation eventually leads to 1.

...,
656,
665,
671,
673,
680,
683,
694,
...

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.

...,
645,
651,
655,
673,
679,
685,
693,
...

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.

...,
667,
669,
671,
673,
675,
677,
679,
...

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.

...,
653,
659,
661,
673,
677,
683,
691,
...

Square-free

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

...,
669,
670,
671,
673,
674,
677,
678,
...

Ulam

The next Ulam number is uniquely the sum of two earlier distinct Ulam numbers.

...,
627,
646,
668,
673,
685,
688,
690,
...

Tanya Khovanova

Number Gossip

Unique Properties of 673

Common Properties of 673