p69.erl

-module(p69).

-export([answer/0]).

%% Euler's Totient function, φ(n) [sometimes called the phi function], is used
%% to determine the number of numbers less than n which are relatively prime to
%% n. For example, as 1, 2, 4, 5, 7, and 8, are all less than nine and
%% relatively prime to nine, φ(9)=6.
%%  n 	Relatively Prime 	φ(n) 	n/φ(n)
%%  2 	1               	1 	2
%%  3 	1,2 	                2 	1.5
%%  4 	1,3 	                2 	2
%%  5 	1,2,3,4 	        4 	1.25
%%  6 	1,5 	                2 	3
%%  7 	1,2,3,4,5,6 	        6 	1.1666...
%%  8 	1,3,5,7 	        4 	2
%%  9 	1,2,4,5,7,8 	        6 	1.5
%% 10 	1,3,7,9 	        4 	2.5
%% It can be seen that n=6 produces a maximum n/φ(n) for n ≤ 10.
%% Find the value of n ≤ 1,000,000 for which n/φ(n) is a maximum.

answer() ->
    lists:foldl(fun(P, Prod) when Prod * P > 1000000 -> Prod;
		   (P, Prod) -> Prod * P
		end, 1, primes:queue(100)).