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 575
- 575 is the smallest number for which the number of divisors and the sum of the distinct prime divisors are both perfect
- 575 is the smallest odious product of 3 evil primes p, q, and r, such that their pairwise products pq, pr, and qr, are also odious
Common Properties of 575
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 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 palindrome is a number that reads the same forward or backward.
Undulating numbers are numbers of the form abababab... in base 10.
This property is significant starting from 3-digit numbers, so we will not consider numbers below 100.