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 190
- 190 is the largest number with only distinct prime Roman numeral palindrome factors that is itself a Roman numeral palindrome (190 = CXC = II * V * XIX)
- 190 is the smallest non-palindrome that shares the number of totatives with its reversal
- 190 is the smallest anagrasum integer: its set of digits is the same as the set of digits that is formed by sums of pairs of its adjacent digits
- 190 is the smallest multiple of 10 such that its digit sum is also a multiple of 10
Common Properties of 190
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.
One can take the sum of the squares of the digits of a number. Those numbers are happy for which iterating this operation eventually leads to 1.
A number is said to be square-free if its prime decomposition contains no repeated factors.
If you start with n points on a line, then draw n-1 points above and between, then n-2 above and between them, and so on, you will get a triangle of points. The number of points in this triangle is a triangle number.
Compare to square, pentagonal and tetrahedral numbers.