77

This number is a composite.

77 is probably the maximal quantity of integers less than 100 that can be arranged in a row such that each is a multiple or a divisor of its neighbors. The solutions is not unique. Here is one due to Dmitry Kamanetsky: 62 31 93 1 57 19 76 38 2 52 26 13 39 78 6 54 27 81 9 63 21 42 84 28 56 14 98 49 7 77 11 99 33 66 22 44 88 8 48 12 36 18 72 24 96 32 64 16 80 40 20 100 50 25 75 15 45 90 30 60 10 70 35 5 85 17 34 68 4 92 46 23 69 3 87 29 58. Missing: 37 41 43 47 51 53 55 59 61 65 67 71 73 74 79 82 83 86 89 91 94 95 97. Can you find a better solution, using 78 or more terms? [Rivera]