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 1540
- 1540 is the smallest number which when multiplied by any repunit prime gives a Smith number
Rare Properties of 1540
A tetrahedral number is the number of balls you can put in a triangular pyramid.
This is the space generalization of triangular and square numbers.
Common Properties of 1540
The number n is abundant if the sum of all its positive divisors except itself is more than n.
They are abundant above perfection, not to mention deficiency. See perfect and deficient numbers.
A positive integer greater than 1 that is not prime is called composite.
Composite numbers are opposite to prime 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 number n is practical if all numbers strictly less than n are sums of distinct divisors of n.
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.