#!/usr/bin/python3.7
import numpy;
import math
from math import sqrt

def generatePrimeNumbers():

    number  = 2
    c = 0

    while True:

        if not (number % 2 == 0 and number > 2):

            for divisor in range(3, int(sqrt(number))+1, 2):
                if number % divisor == 0:
                    c = 1
                    break

            if  c != 1:
                yield number

        number += 1
        c = 0

def getPrimeFactors(multiple):

    primeNumbers = generatePrimeNumbers()

    output = []

    while multiple > 1:

        factor = next(primeNumbers)

        if multiple % factor == 0:
            output.append(factor)
            multiple /= factor
            primeNumbers = generatePrimeNumbers()
        else:
            continue

    return output



def generateSequence(k):
    x = [0,0.5]
    for i in range(2,k):
        xi = 1;
        factors = getPrimeFactors(i);

        for factor in factors:

            sumprev = 0;

            for i in range(1,factor):
                if factor != k and factor != 1:
                    sumprev -= x[i]

            xi *= sumprev

        x.append(xi)
    return x;


#seq = generateSequence(97);
#print(seq);
#print(sum(seq))