Erlang Assignment 1: Number Personalities
Fall 2010, David Matuszek

Purposes of this assignment:

General idea of the assignment:

For each of the numbers in a given range, determine some characteristics of those numbers. Print out the numbers, one per line, along with a list of its characteristics (on the same line).

Your output should look approximately like this:

 1  [happy,triangular,square,antifirst]
2 [prime,smug,antifirst]
3 [prime,triangular]
4 [square,antifirst] ...

Details:

General

Write the following functions, along with any helper functions you may need.

Prime and composite numbers

A positive number is prime if its only positive divisors are itself and one. For example, 7 is prime because it is evenly divisible by 1 and 7, but not by any number in between (in particular, it is not evenly divisible by 2, 3, 4, 5, or 6).

A positive number is composite if it is not prime. For example, 10 is composite because it is evenly divisible by 2 and 5; 12 is composite because it is evenly divisible by 2, 3, 4, and 6. As a special case, 1 is considered to be composite.

Happy and unhappy numbers

Repeatedly apply the following procedure to a number:

  1. Square each of the digits of the number.
  2. Add the squares together.

If by doing this you eventually get to 1, then the number is happy.

For example, if you start with 19:

If instead you get into an infinite loop, the number is unhappy. So if your program runs forever, the number is unhappy. This isn't a very useful test, however. Fortunately, every unhappy number will eventually get into this cycle:

4, 16, 37, 58, 89, 145, 42, 20, 4, ...

so if you get any one of these numbers, say 4, then you can stop and conclude that the number is unhappy.

Triangular numbers

stacks of ballsA triangular number is a number of the form 1 + 2 + 3 + ... + n, for some positive n. These numbers are called triangular because, if you have that many objects, you can arrange them in an equilateral triangle (see figure).

The first few triangular numbers are 1, 3, 6, 10, 15....

Square numbers

A square number is a number of the form 1 + 3 + 5 + 7 + ... + n, for some odd positive n. (The figure should help you understand why this definition is the same as the usual definition of square numbers.) Use this definition in your program, rather than some other way to determine if a number is a square number.

Balls in a square

Smug numbers

A number is smug if it is the sum of two square numbers. The first few smug numbers are 2 (1+1), 5 (1+4), 8 (4+4), 10 (1+9), 13 (4+9), etc.

Abundant numbers

A number is abundant if the sum of its proper divisors (including 1, but excluding the number itself) is greater than the number. The first few abundant numbers are 12 (1+2+3+4+6=14), 18 (1+2+3+6+9=21), 20 (1+2+4+5+10=24), and 24 (1+2+3+4+6+8+12=36).

Antifirst numbers

A number is antifirst if it has more divisors than any preceding (positive) number. The first few antifirst numbers are 1 (the only divisor is 1), 2 (two divisors, 1 and 2), 4 (1, 2, 4), 6 (1, 2, 3, 6), 12 (1, 2, 3, 4, 6, 12), and 24 (1, 2, 3, 4, 6, 8, 12, 24) .

Due date:

Turn in your numpers.erl file by midnight, Thursday Sept. 30 . As only one file is required, there is no need to zip it.