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 1441

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.

...,
1177,
1235,
1294,
1441,
1443,
1574,
1595,
...

Common Properties of 1441

Composite

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

Composite numbers are opposite to prime numbers.

...,
1437,
1438,
1440,
1441,
1442,
1443,
1444,
...

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.

...,
1437,
1438,
1439,
1441,
1442,
1443,
1444,
...

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.