# What is the sum of all positive integers less than LaTeX: $10^4$ which are relatively prime to LaTeX: $10^4?$

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 def num_factors(n, p, rpt): results = [] for i in range(1, int(n**0.5) + 1): if n % i == 0: if n == p: rpt.append(i) rpt.append(int(n/i)) results.append(i) results.append(int(n/i)) if n == p: rpt = sorted(set(rpt)) rpt = rpt[1:] results = sorted(set(results)) results = results[1:] k = set(results).intersection(set(rpt)) # print k if len(k) == 0: numbers.append(n) return numbers ################################################################# p = 10000 r_p_to = [] # relatively prime to numbers = [] for j in range (p, 0, -1): l = num_factors(j, p, r_p_to) print sorted(l) print 'Number of positive integers relatively prime to %d: %d' %( p, len(l)) print 'Sum of positive integers relatively prime to %d: %d' %( p, sum(l)) 

[1, 3, 7, 9, 11, 13, 17, ......................................................, 9977, 9979, 9981, 9983, 9987, 9989, 9991, 9993, 9997, 9999]

Number of positive integers relatively prime to 10000: 4000 Sum of positive integers relatively prime to 10000: 20000000 Note by Michael Fitzgerald
3 years, 5 months ago

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