The number of unique n-point stars that can be drawn is related to phi(n), the totient of n. The totient of n is the number of numbers that are "coprimes" of n. This means they have no common factors with n. The number 60 has the following coprimes: 1 7 11 13 17 19 23 29 31 37 41 43 47 49 53 59 It can be shown that phi(n) = n * (p1-1)/p1 * (p2-1)/p2 ... where the p's range over the unique prime factors of n. The number of n-point stars = (phi(n)-2)/2 Since 60 = 2 * 2 * 3 * 5, we have phi(60) = 60 * 1/2 * 2/3 * 4/5 = 16 The number of unique 60-point stars = (16-2)/2 = 7 totient.tc D:\my-git-repo>tc totient.tc *** TINY-C VERSION 1.0, COPYRIGHT 1977, T A GIBSON *** This C version copyright 2017, T A Gibson totient of 5 is 4 number of 5 point stars is 1 totient of 6 is 2 number of 6 point stars is 0 totient of 7 is 6 number of 7 point stars is 2 totient of 8 is 4 number of 8 point stars is 1 totient of 9 is 6 number of 9 point stars is 2 totient of 10 is 4 number of 10 point stars is 1 totient of 11 is 10 number of 11 point stars is 4 totient of 12 is 4 number of 12 point stars is 1 totient of 13 is 12 number of 13 point stars is 5 totient of 14 is 6 number of 14 point stars is 2 totient of 15 is 8 number of 15 point stars is 3 totient of 16 is 8 number of 16 point stars is 3 totient of 17 is 16 number of 17 point stars is 7 totient of 18 is 6 number of 18 point stars is 2 totient of 19 is 18 number of 19 point stars is 8 totient of 20 is 8 number of 20 point stars is 3 totient of 21 is 12 number of 21 point stars is 5 totient of 22 is 10 number of 22 point stars is 4 totient of 23 is 22 number of 23 point stars is 10 totient of 24 is 8 number of 24 point stars is 3 totient of 25 is 20 number of 25 point stars is 9 totient of 26 is 12 number of 26 point stars is 5 totient of 27 is 18 number of 27 point stars is 8 totient of 28 is 12 number of 28 point stars is 5 totient of 29 is 28 number of 29 point stars is 13 totient of 30 is 8 number of 30 point stars is 3 totient of 31 is 30 number of 31 point stars is 14 totient of 32 is 16 number of 32 point stars is 7 totient of 33 is 20 number of 33 point stars is 9 totient of 34 is 16 number of 34 point stars is 7 totient of 35 is 24 number of 35 point stars is 11 totient of 36 is 12 number of 36 point stars is 5 totient of 37 is 36 number of 37 point stars is 17 totient of 38 is 18 number of 38 point stars is 8 totient of 39 is 24 number of 39 point stars is 11 totient of 40 is 16 number of 40 point stars is 7 totient of 41 is 40 number of 41 point stars is 19 totient of 42 is 12 number of 42 point stars is 5 totient of 43 is 42 number of 43 point stars is 20 totient of 44 is 20 number of 44 point stars is 9 totient of 45 is 24 number of 45 point stars is 11 totient of 46 is 22 number of 46 point stars is 10 totient of 47 is 46 number of 47 point stars is 22 totient of 48 is 16 number of 48 point stars is 7 totient of 49 is 42 number of 49 point stars is 20 totient of 50 is 20 number of 50 point stars is 9 totient of 51 is 32 number of 51 point stars is 15 totient of 52 is 24 number of 52 point stars is 11 totient of 53 is 52 number of 53 point stars is 25 totient of 54 is 18 number of 54 point stars is 8 totient of 55 is 40 number of 55 point stars is 19 totient of 56 is 24 number of 56 point stars is 11 totient of 57 is 36 number of 57 point stars is 17 totient of 58 is 28 number of 58 point stars is 13 totient of 59 is 58 number of 59 point stars is 28 totient of 60 is 16 number of 60 point stars is 7 totient of 61 is 60 number of 61 point stars is 29 totient of 62 is 30 number of 62 point stars is 14 totient of 63 is 36 number of 63 point stars is 17 totient of 64 is 32 number of 64 point stars is 15 totient of 65 is 48 number of 65 point stars is 23 totient of 66 is 20 number of 66 point stars is 9 totient of 67 is 66 number of 67 point stars is 32 totient of 68 is 32 number of 68 point stars is 15 totient of 69 is 44 number of 69 point stars is 21 totient of 70 is 24 number of 70 point stars is 11 totient of 71 is 70 number of 71 point stars is 34 totient of 72 is 24 number of 72 point stars is 11 totient of 73 is 72 number of 73 point stars is 35 totient of 74 is 36 number of 74 point stars is 17 totient of 75 is 40 number of 75 point stars is 19 totient of 76 is 36 number of 76 point stars is 17 totient of 77 is 60 number of 77 point stars is 29 totient of 78 is 24 number of 78 point stars is 11 totient of 79 is 78 number of 79 point stars is 38 totient of 80 is 32 number of 80 point stars is 15 totient of 81 is 54 number of 81 point stars is 26 totient of 82 is 40 number of 82 point stars is 19 totient of 83 is 82 number of 83 point stars is 40 totient of 84 is 24 number of 84 point stars is 11 totient of 85 is 64 number of 85 point stars is 31 totient of 86 is 42 number of 86 point stars is 20 totient of 87 is 56 number of 87 point stars is 27 totient of 88 is 40 number of 88 point stars is 19 totient of 89 is 88 number of 89 point stars is 43 totient of 90 is 24 number of 90 point stars is 11 totient of 91 is 72 number of 91 point stars is 35 totient of 92 is 44 number of 92 point stars is 21 totient of 93 is 60 number of 93 point stars is 29 totient of 94 is 46 number of 94 point stars is 22 totient of 95 is 72 number of 95 point stars is 35 totient of 96 is 32 number of 96 point stars is 15 totient of 97 is 96 number of 97 point stars is 47 totient of 98 is 42 number of 98 point stars is 20 totient of 99 is 60 number of 99 point stars is 29 totient of 100 is 40 number of 100 point stars is 19 totient of 101 is 100 number of 101 point stars is 49 done |