public static long Solution()
{
var stopwatch = new System.Diagnostics.Stopwatch();
long solution = 0;
var divisorsOfOrder = UtilityFunctions.Divisors(order);
var primes = UtilityFunctions.Primes((int)Math.Sqrt(UtilityFunctions.IntegralPower(2, order / 2) + 1));
var primeFactors = UtilityFunctions.PrimeFactors(UtilityFunctions.IntegralPower(2, order) - 1, primes);
var reducedPrimes = primeFactors.Select(t => t.Item1).ToList();
foreach (var d in divisorsOfOrder)
{
var m = UtilityFunctions.Moebius(d, null, primes);
if (m != 0)
{
var divisorsOfPowerOfTwo = UtilityFunctions.Divisors(UtilityFunctions.IntegralPower(2, order / d) - 1, null, reducedPrimes);
solution += (divisorsOfPowerOfTwo.Sum() + divisorsOfPowerOfTwo.Count()) * m;
}
}
return(solution);
}