## Special Numbers

Monday, January 15, 2024

Lots of numbers are special in various definitions of specialness. This often forms the basis of different programming challenges. In the case of the most recent Perl Weekly Challenge #252, the problem statement declares that a number is “special” in this way:

You are given an array of integers,

`@ints`

.Write a script to find the sum of the squares of all special elements of the given array.

An element

`$int[i]`

of`@ints`

is called special if`i`

divides`n`

, i.e.`n % i == 0`

, where`n`

is the length of the given array. Also the array is 1-indexed for the task.

And it gives two examples, which we can use as test cases later when we solve this in Factor.

**Spoiler Alert**: This weekly challenge deadline is due in a few days from now
(on January 21, 2024 at 23:59). This blog post provides some solutions to this
challenge. Please don’t read on if you intend to complete the challenge on your
own.

## Solution

Let’s find the special indices – which are just the divisors of the length of the input sequence – and then take the elements at those special indices:

```
: special-numbers ( ints -- ints' )
[ length divisors 1 v-n ] [ nths ] bi ;
```

And so, we can solve this problem for both provided examples:

```
{ 21 } [ { 1 2 3 4 } special-numbers sum-of-squares ] unit-test
{ 63 } [ { 2 7 1 19 18 3 } special-numbers sum-of-squares ] unit-test
```

And a “script”, if we wanted to take input from the command-line, as requested:

```
MAIN: [
[ readln ] [
split-words harvest [ string>number ] map
dup special-numbers sum-of-squares
"%u => %u\n" printf
] while*
]
```