10^n以内，含不同因子最多的是哪三个连续自然数？

northwolves

在三个连续自然数中，含不同因子最多的数是哪些数，在小于10^2，10^3，10^4的范围内？

我的回复如下，

{1,{6,7,8},7}

{2,{70,71,72}, 19}

{3,{720,721,722}, 37}

{4,{8398,8399,8400}, 77}

{5,{83160,83161,83162}, 137}

{6,{720718,720718,720720}, 253}

{7,{8648639,8648640,8648641}, 458}

{8,{98017918,98017919,98017920}, 785}

{9,{994593600,994593601,994593602}, 1365}

{10,{9311702398, 9311702399, 9311702400}, 2365}

{11,{96376119838, 96376119839, 96376119840}, 3857}

{12,{963761198400, 963761198401, 963761198402}, 6737}

{13,{9316358251200, 9316358251201, 9316358251202}, 10773}

{14,{97821761637600, 97821761637601, 97821761637602}, 17289}

{15,{978217616375998, 978217616375999, 978217616376000}, 26897}

{16,{9651747148243198, 9651747148243199, 9651747148243200}, 41509}

{17,{90974238322967999, 90974238322968000, 90974238322968001}, 64542}

{18,{994651672331116798, 994651672331116799, 994651672331116800}, 103701}

{19,{9649334211456139198,9649334211456139199,9649334211456139200},161313}

{20,{96493342114561392000,96493342114561392001,96493342114561392002},245781}

n=1-11是穷举比较过的，应该没问题。

n=12-20 通过素因子进行了初筛，如何确定是不是真正的不同因子最多的三个数？