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 370
- 370 is the smallest sum of two primes squares that is also a sum of two primes cubes (370 = 32+192 = 33+73)
- 370 is the smallest non-repdigit number that is the average of the numbers formed by all permutations of its digits (370 = (073+037+307+370+703+730)/6)
- 370 is one of four numbers that equals the sum of the cubes of its digits: 370 = 33 + 73 + 03
Rare Properties of 370
A k-digit number n is called narcissistic if it is equal to the sum of k-th powers of its digits. They are also called Plus Perfect numbers.
Common Properties of 370
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.