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 412
- 412 is the smallest number n such that the sums of prime factors, ignoring multiplicity, of σ(n) and φ(n) are equal to each other but the sets of prime factors of σ(n) and φ(n) are different
- 412 is the largest determinant of a 3-by-3 matrix containing distinct digits 1 through 9
Common Properties of 412
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.
The next Ulam number is uniquely the sum of two earlier distinct Ulam numbers.