Кортежи 3-24 и 3-96 - возможно
Да, см ниже.
Код:
Pat/10^ 10
3- 12 5427928
3- 24 5429016
3- 36 5429545
3- 48 5428800
3- 72 5431499
3- 96 5428980
3-108 5433210
Pat/10^ 10
3- 84 8140849
3-168 81
3-252 8147636
Pat/10^ 10
3-132 6787112
3-264 67
Pat/10^ 10
3-156 61
19-252 и 19-828 - не уверен.
Не будут совпадать, потому что у диаметров разные простые делители: 7 и 23 соответственно. А зависимость количества всех кортежей от простых делителей диаметра оказывается такая:
Код:
2,3 5 7 11 13
100 200 150 125 112.5
Именно совпадения редки, среднее количество всех кортежей проседает с ростом диаметра:
Код:
1 12 1 e6: sum = 2900, sred = 2900.000000000000000000000000
2 24 1 e6: sum = 2820, sred = 2860.000000000000000000000000
3 36 1 e6: sum = 2864, sred = 2861.333333333333333333333333
4 48 1 e6: sum = 2816, sred = 2850.000000000000000000000000
5 72 1 e6: sum = 2831, sred = 2846.200000000000000000000000
6 96 1 e6: sum = 2861, sred = 2848.666666666666666666666667
7 108 1 e6: sum = 2900, sred = 2856.000000000000000000000000
8 144 1 e6: sum = 2882, sred = 2859.250000000000000000000000
9 192 1 e6: sum = 2878, sred = 2861.333333333333333333333333
10 216 1 e6: sum = 2918, sred = 2867.000000000000000000000000
11 288 1 e6: sum = 2829, sred = 2863.545454545454545454545455
12 324 1 e6: sum = 2800, sred = 2858.250000000000000000000000
13 384 1 e6: sum = 2910, sred = 2862.230769230769230769230769
14 432 1 e6: sum = 2823, sred = 2859.428571428571428571428571
15 576 1 e6: sum = 2857, sred = 2859.266666666666666666666667
16 648 1 e6: sum = 2877, sred = 2860.375000000000000000000000
17 768 1 e6: sum = 2816, sred = 2857.764705882352941176470588
18 864 1 e6: sum = 2795, sred = 2854.277777777777777777777778
19 972 1 e6: sum = 2769, sred = 2849.789473684210526315789474
20 1152 1 e6: sum = 2830, sred = 2848.800000000000000000000000
21 1296 1 e6: sum = 2853, sred = 2849.000000000000000000000000
22 1536 1 e6: sum = 2832, sred = 2848.227272727272727272727273
23 1728 1 e6: sum = 2891, sred = 2850.086956521739130434782609
24 1944 1 e6: sum = 2784, sred = 2847.333333333333333333333333
25 2304 1 e6: sum = 2824, sred = 2846.400000000000000000000000
26 2592 1 e6: sum = 2859, sred = 2846.884615384615384615384615
27 2916 1 e6: sum = 2846, sred = 2846.851851851851851851851852
28 3072 1 e6: sum = 2769, sred = 2844.071428571428571428571429
29 3456 1 e6: sum = 2790, sred = 2842.206896551724137931034483
30 3888 1 e6: sum = 2800, sred = 2840.800000000000000000000000
31 4608 1 e6: sum = 2811, sred = 2839.838709677419354838709677
32 5184 1 e6: sum = 2839, sred = 2839.812500000000000000000000
33 5832 1 e6: sum = 2878, sred = 2840.969696969696969696969697
34 6144 1 e6: sum = 2789, sred = 2839.441176470588235294117647
35 6912 1 e6: sum = 2791, sred = 2838.057142857142857142857143
36 7776 1 e6: sum = 2848, sred = 2838.333333333333333333333333
37 8748 1 e6: sum = 2836, sred = 2838.270270270270270270270270
38 9216 1 e6: sum = 2795, sred = 2837.131578947368421052631579
39 10368 1 e6: sum = 2799, sred = 2836.153846153846153846153846
40 11664 1 e6: sum = 2816, sred = 2835.650000000000000000000000
41 12288 1 e6: sum = 2823, sred = 2835.341463414634146341463415
42 13824 1 e6: sum = 2791, sred = 2834.285714285714285714285714
43 15552 1 e6: sum = 2776, sred = 2832.930232558139534883720930
44 17496 1 e6: sum = 2724, sred = 2830.454545454545454545454545
45 18432 1 e6: sum = 2826, sred = 2830.355555555555555555555556
46 20736 1 e6: sum = 2813, sred = 2829.978260869565217391304348
47 23328 1 e6: sum = 2741, sred = 2828.085106382978723404255319
48 24576 1 e6: sum = 2795, sred = 2827.395833333333333333333333
49 26244 1 e6: sum = 2731, sred = 2825.428571428571428571428571
50 27648 1 e6: sum = 2702, sred = 2822.960000000000000000000000
51 31104 1 e6: sum = 2734, sred = 2821.215686274509803921568627
52 34992 1 e6: sum = 2677, sred = 2818.442307692307692307692308
53 36864 1 e6: sum = 2800, sred = 2818.094339622641509433962264
54 41472 1 e6: sum = 2668, sred = 2815.314814814814814814814815
55 46656 1 e6: sum = 2741, sred = 2813.963636363636363636363636
56 49152 1 e6: sum = 2681, sred = 2811.589285714285714285714286
57 52488 1 e6: sum = 2653, sred = 2808.807017543859649122807018
58 55296 1 e6: sum = 2767, sred = 2808.086206896551724137931035
59 62208 1 e6: sum = 2717, sred = 2806.542372881355932203389831
60 69984 1 e6: sum = 2657, sred = 2804.050000000000000000000000
61 73728 1 e6: sum = 2732, sred = 2802.868852459016393442622951
62 78732 1 e6: sum = 2728, sred = 2801.661290322580645161290323
63 82944 1 e6: sum = 2723, sred = 2800.412698412698412698412698
64 93312 1 e6: sum = 2717, sred = 2799.109375000000000000000000
65 98304 1 e6: sum = 2623, sred = 2796.400000000000000000000000