PWC109 - Chowla Numbers


Here we are with TASK #1 from the Perl Weekly Challenge #109. Enjoy!

The challenge

Write a script to generate first 20 Chowla Numbers, named after, Sarvadaman D. S. Chowla, a London born Indian American mathematician. It is defined as:

C(n) = (sum of divisors of n) - 1 - n

The questions

The first question is a picky one… the definition above isn’t really correct, is it?!? I mean, if we apply it to $n = 1$, technically speaking we get $-1$, so it’s a good approximation.

Hence, I’ll refer to the definition in Rosetta code:

The chowla number of $n$ is (as defined by Chowla’s function):

  • the sum of the divisors of $n$ excluding unity and $n$
  • where $n$ is a positive integer

Then I guess we should start counting from $n = 1$ for taking the first $20$ elements, right?

The solution

I was a bit surprised when I found out that it’s possible to code a very compact solution:

#!/usr/bin/env perl
use 5.024;
use warnings;
use experimental qw< postderef signatures >;
no warnings qw< experimental::postderef experimental::signatures >;
use List::Util 'sum';

sub gcd { my ($A, $B) = @_; ($A, $B) = ($B % $A, $A) while $A; return $B }

sub chowla_number ($n) { sum(grep { gcd($n, $_) == $_ } 2 .. $n - 1) // 0 }

say join ', ', map { chowla_number($_) } 1 .. 20;

It’s tremendously inefficient but fits within the number of columns I use as limit for coding subs as one-liners 🙄 Moreover… it’s only 20 items, right?

Stay safe!

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