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 170
- 170 is the smallest composite number such that exactly four distinct permutations of its decimal digits are prime (17, 71, 107, and 701 are all prime)
- 170 can be written as (22 + 3)2 + (32 + 2)2)
- 170 is the smallest number n, except 1, for which φ(n) and σ(n) are both square
- 170 is the smallest sphenic number (the product of three distinct primes) with no squarefree neighbors: 169 = 132, 170 = 2 * 5 * 17, and 171 = 32 * 19 (submitted by Massimo Kofler)
Common Properties of 170
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 evil if it has an even number of 1's in its binary expansion.
Guess what odious numbers are.
A number is said to be square-free if its prime decomposition contains no repeated factors.