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 62
- 62 is the smallest inconsummate number in base 10: no number is a 62-multiple of the sum of its digits
- 62 is the only number whose cube (238328) consists of 3 digits each occurring 2 times
- 62 is the smallest number that can be written as the sum of 3 distinct squares in 2 ways: 62 = 12 + 52 + 62 = 22 + 32 + 72
Common Properties of 62
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.
A number is even if it is divisible by 2.
Numbers that are not even are odd. 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 number is said to be square-free if its prime decomposition contains no repeated factors.
The next Ulam number is uniquely the sum of two earlier distinct Ulam numbers.