Number Gossip
(Enter a number and I'll tell you everything you wanted to know about it but were afraid to ask.)
Rare Properties of 8545
The number n is called an aspiring number if its aliquot sequence terminates in a perfect number, and it is not a perfect number itself.
Common Properties of 8545
The number n is called an apocalyptic power if 2n contains the consecutive digits 666 (in decimal).
A positive integer greater than 1 that is not prime is called composite.
Composite numbers are opposite to prime numbers.
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.
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.
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.
The number n is odious if it has an odd number of 1's in its binary expansion.
Guess what evil numbers are.
A composite number is called a Smith number if the sum of its digits equals the sum of all the digits appearing in its prime divisors (counting multiplicity).
In 1984, when Albert Wilansky called his brother-in-law, named Smith, he noticed that the phone number possesses the property described here. Are they called joke numbers, because they were named after an innocent unsuspecting brother-in-law :-) ?
A number is said to be square-free if its prime decomposition contains no repeated factors.