Haskell

#22 Names scores - Project Euler. projecteuler.net . Accessed Feb 18, 2022.

Problem Statement

Using names.txt, a 46K text file containing over 5,000 first names, begin by sorting it into alphabetical order. Then working out the alphabetical value for each name, multiply this value by its alphabetical position in the list to obtain a name score.

For example, when the list is sorted into alphabetical order, COLIN, which is worth \(3 + 15 + 12 + 9 + 14 = 53\), is the 938th name in the list. So COLIN would obtain a score of \(938 \times 53 = 49{,}714\).

Problem Statement

Let \(d(n)\) be defined as the sum of proper divisors of \(n\) (numbers less than \(n\) which divide evenly into \(n\)).

If \(d(a) = b\) and \(d(b) = a\), where \(a \neq b\), then \(a\) and \(b\) are an amicable pair and each of \(a\) and \(b\) are called amicable numbers.

For example, the proper divisors of \(220\) are \(1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110\); therefore \(d(220) = 284\). The proper divisors of \(284\) are \(1, 2, 4, 71, 142\); so \(d(284) = 220\).