160106(3)

Ruby


異なる単位分数（< 1）の和が1 より大きい自然数(2)

異なる単位分数（< 1）の和が1 より大きい自然数となるもののうち、
分母の和が最小になるのは次の場合である。
2
= 1 / 2 + 1 / 3 + 1 / 4 + 1 / 5 + 1 / 6 + 1 / 8 + 1 / 9 + 1 / 10 + 1 / 15 + 1 / 18 + 1 / 20 + 1 / 24
（ちなみに、分母の和は124）
このことを次のコードで見つけた。

# 和因子はmin以上max以下で互いに異なる
def partition(n, min, max)
  return [[]] if n == 0
  [max, n].min.downto(min).flat_map{|i| partition(n - i, min, i - 1).map{|rest| [i, *rest]}}
end

(2..135).each{|n|
  p_ary = []
  partition(n, 2, n).each{|ary|
    a = ary.inject(0){|s, i| s + 1 / i.to_r}
    p_ary << [a.numerator, ary] if a.denominator == 1
  }
  p [n, p_ary]
}

出力結果
[2, []]
[3, []]
[4, []]
[5, []]
[6, []]
[7, []]
[8, []]
[9, []]
[10, []]
[11, [[1, [6, 3, 2]]]]
[12, []]
[13, []]
[14, []]
[15, []]
[16, []]
[17, []]
[18, []]
[19, []]
[20, []]
[21, []]
[22, []]
[23, []]
[24, [[1, [12, 6, 4, 2]]]]
[25, []]
[26, []]
[27, []]
[28, []]
[29, []]
[30, [[1, [15, 10, 3, 2]]]]
[31, [[1, [20, 5, 4, 2]]]]
[32, [[1, [18, 9, 3, 2]]]]
[33, []]
[34, []]
[35, []]
[36, []]
[37, [[1, [24, 8, 3, 2]]]]
[38, [[1, [20, 6, 5, 4, 3]]]]
[39, []]
[40, []]
[41, []]
[42, []]
[43, [[1, [15, 12, 10, 4, 2]]]]
[44, []]
[45, [[1, [20, 12, 6, 5, 2]], [1, [18, 12, 9, 4, 2]]]]
[46, []]
[47, []]
[48, []]
[49, []]
[50, [[1, [24, 12, 8, 4, 2]], [1, [15, 12, 10, 6, 4, 3]]]]
[51, []]
[52, [[1, [18, 12, 9, 6, 4, 3]]]]
[53, [[1, [30, 10, 6, 5, 2]]]]
[54, [[1, [42, 7, 3, 2]]]]
[55, [[1, [28, 14, 7, 4, 2]]]]
[56, []]
[57, [[1, [24, 12, 8, 6, 4, 3]], [1, [20, 15, 10, 5, 4, 3]]]]
[58, []]
[59, [[1, [20, 18, 9, 5, 4, 3]]]]
[60, [[1, [18, 15, 10, 9, 6, 2]]]]
[61, [[1, [28, 21, 6, 4, 2]]]]
[62, [[1, [30, 20, 6, 4, 2]], [1, [28, 14, 7, 6, 4, 3]]]]
[63, []]
[64, [[1, [40, 10, 8, 4, 2]], [1, [30, 12, 10, 5, 4, 3]], [1, [24, 20, 8, 5, 4, 3]], [1, [20, 15, 12, 10, 5, 2]]]]
[65, [[1, [24, 15, 10, 8, 6, 2]]]]
[66, [[1, [36, 18, 6, 4, 2]], [1, [28, 21, 12, 3, 2]], [1, [20, 18, 12, 9, 5, 2]]]]
[67, [[1, [45, 9, 6, 5, 2]], [1, [42, 12, 7, 4, 2]], [1, [30, 20, 12, 3, 2]], [1, [24, 18, 9, 8, 6, 2]]]]
[68, []]
[69, [[1, [35, 15, 14, 3, 2]], [1, [28, 14, 12, 7, 6, 2]]]]
[70, []]
[71, [[1, [40, 10, 8, 6, 4, 3]], [1, [36, 18, 12, 3, 2]], [1, [33, 22, 11, 3, 2]], [1, [24, 20, 12, 8, 5, 2]], [1, [20, 15, 12, 10, 6, 5, 3]], [1, [18, 15, 12, 10, 9, 4, 3]]]]
[72, []]
[73, [[1, [20, 18, 12, 9, 6, 5, 3]]]]
[74, [[1, [42, 12, 7, 6, 4, 3]], [1, [30, 18, 10, 9, 5, 2]]]]
[75, [[1, [40, 15, 8, 5, 4, 3]]]]
[76, [[1, [48, 16, 6, 4, 2]], [1, [28, 20, 14, 7, 5, 2]], [1, [24, 15, 12, 10, 8, 4, 3]]]]
[77, []]
[78, [[1, [45, 12, 9, 5, 4, 3]], [1, [40, 12, 10, 8, 6, 2]], [1, [24, 20, 12, 8, 6, 5, 3]], [1, [24, 18, 12, 9, 8, 4, 3]]]]
[79, [[1, [40, 24, 10, 3, 2]], [1, [30, 24, 10, 8, 5, 2]]]]
[80, [[1, [28, 21, 15, 10, 4, 2]]]]
[81, [[1, [48, 16, 12, 3, 2]], [1, [42, 20, 7, 5, 4, 3]], [1, [30, 20, 15, 10, 4, 2]], [1, [30, 18, 10, 9, 6, 5, 3]], [1, [28, 15, 14, 10, 7, 4, 3]]]]
[82, [[1, [42, 15, 10, 7, 6, 2]], [1, [40, 15, 12, 8, 5, 2]], [1, [35, 15, 14, 12, 4, 2]], [1, [28, 21, 20, 6, 5, 2]], [1, [28, 21, 18, 9, 4, 2]]]]
[83, [[1, [30, 20, 18, 9, 4, 2]], [1, [28, 20, 14, 7, 6, 5, 3]], [1, [28, 18, 14, 9, 7, 4, 3]]]]
[84, [[1, [42, 18, 9, 7, 6, 2]], [1, [33, 22, 12, 11, 4, 2]]]]
[85, [[1, [40, 20, 10, 8, 5, 2]], [1, [36, 18, 15, 10, 4, 2]], [1, [35, 20, 14, 10, 4, 2]]]]
[86, [[1, [45, 15, 10, 9, 5, 2]], [1, [30, 24, 10, 8, 6, 5, 3]], [1, [24, 18, 15, 10, 9, 8, 2]]]]
[87, [[1, [60, 15, 6, 4, 2]], [1, [36, 20, 18, 6, 5, 2]], [1, [28, 24, 21, 8, 4, 2]], [1, [28, 21, 15, 10, 6, 4, 3]], [1, [20, 18, 15, 10, 9, 6, 5, 4]]]]
[88, [[1, [42, 20, 12, 7, 5, 2]], [1, [30, 24, 20, 8, 4, 2]], [1, [30, 20, 15, 10, 6, 4, 3]], [1, [28, 24, 14, 8, 7, 4, 3]], [1, [28, 15, 14, 12, 10, 7, 2]]]]
[89, [[1, [45, 30, 9, 3, 2]], [1, [42, 24, 8, 7, 6, 2]], [1, [40, 15, 12, 8, 6, 5, 3]], [1, [35, 15, 14, 12, 6, 4, 3]], [1, [28, 21, 18, 9, 6, 4, 3]]]]
[90, [[1, [30, 20, 18, 9, 6, 4, 3]], [1, [28, 18, 14, 12, 9, 7, 2]]]]
[91, [[1, [33, 22, 12, 11, 6, 4, 3]]]]
[92, [[1, [60, 15, 12, 3, 2]], [1, [45, 36, 5, 4, 2]], [1, [40, 24, 15, 6, 5, 2]], [1, [40, 24, 12, 10, 4, 2]], [1, [40, 20, 10, 8, 6, 5, 3]], [1, [40, 18, 10, 9, 8, 4, 3]], [1, [36, 24, 18, 8, 4, 2]], [1, [36, 18, 15, 10, 6, 4, 3]], [1, [35, 30, 14, 6, 5, 2]], [1, [35, 20, 14, 10, 6, 4, 3]], [1, [24, 20, 15, 10, 8, 6, 5, 4]], [1, [20, 18, 15, 12, 10, 9, 5, 3]]]]
[93, [[1, [45, 24, 9, 8, 5, 2]], [1, [45, 15, 10, 9, 6, 5, 3]], [1, [42, 15, 12, 10, 7, 4, 3]], [1, [28, 21, 20, 12, 5, 4, 3]], [1, [24, 18, 15, 10, 9, 8, 6, 3]]]]
[94, [[1, [30, 18, 12, 10, 9, 6, 5, 4]], [1, [28, 24, 21, 8, 6, 4, 3]], [1, [28, 21, 15, 12, 10, 6, 2]], [1, [24, 20, 18, 9, 8, 6, 5, 4]]]]
[95, [[1, [72, 9, 8, 4, 2]], [1, [60, 20, 10, 3, 2]], [1, [54, 27, 9, 3, 2]], [1, [48, 16, 15, 10, 4, 2]], [1, [45, 20, 15, 9, 4, 2]], [1, [42, 20, 12, 7, 6, 5, 3]], [1, [42, 18, 12, 9, 7, 4, 3]], [1, [30, 24, 20, 8, 6, 4, 3]], [1, [30, 20, 15, 12, 10, 6, 2]], [1, [28, 24, 14, 12, 8, 7, 2]], [1, [28, 15, 14, 12, 10, 7, 6, 3]]]]
[96, [[1, [42, 30, 10, 7, 5, 2]], [1, [35, 20, 15, 14, 5, 4, 3]], [1, [28, 21, 18, 12, 9, 6, 2]], [1, [28, 20, 14, 12, 7, 6, 5, 4]]]]
[97, [[1, [48, 20, 16, 6, 5, 2]], [1, [48, 18, 16, 9, 4, 2]], [1, [30, 20, 18, 12, 9, 6, 2]], [1, [28, 18, 14, 12, 9, 7, 6, 3]], [1, [24, 20, 15, 12, 10, 8, 5, 3]]]]
[98, [[1, [36, 20, 18, 12, 5, 4, 3]], [1, [33, 22, 20, 11, 5, 4, 3]]]]
[99, [[1, [45, 36, 6, 5, 4, 3]], [1, [40, 30, 15, 8, 4, 2]], [1, [40, 24, 12, 10, 6, 4, 3]], [1, [40, 18, 12, 10, 9, 8, 2]], [1, [36, 24, 18, 8, 6, 4, 3]], [1, [36, 18, 15, 12, 10, 6, 2]], [1, [35, 20, 14, 12, 10, 6, 2]], [1, [35, 18, 15, 14, 9, 6, 2]], [1, [33, 22, 15, 11, 10, 6, 2]], [1, [30, 24, 12, 10, 8, 6, 5, 4]], [1, [24, 20, 18, 12, 9, 8, 5, 3]]]]
[100, [[1, [56, 21, 8, 7, 6, 2]], [1, [45, 24, 9, 8, 6, 5, 3]], [1, [42, 24, 12, 8, 7, 4, 3]]]]
[101, [[1, [60, 30, 5, 4, 2]], [1, [33, 22, 18, 11, 9, 6, 2]], [1, [30, 28, 21, 10, 5, 4, 3]], [1, [28, 24, 21, 12, 8, 6, 2]], [1, [28, 21, 20, 15, 10, 5, 2]]]]
[102, [[1, [72, 9, 8, 6, 4, 3]], [1, [48, 24, 16, 8, 4, 2]], [1, [48, 16, 15, 10, 6, 4, 3]], [1, [45, 30, 12, 9, 4, 2]], [1, [45, 20, 15, 9, 6, 4, 3]], [1, [30, 24, 20, 12, 8, 6, 2]], [1, [28, 24, 14, 12, 8, 7, 6, 3]], [1, [28, 20, 15, 14, 10, 7, 5, 3]]]]
[103, [[1, [42, 30, 10, 7, 6, 5, 3]], [1, [42, 18, 15, 10, 9, 7, 2]], [1, [40, 35, 14, 8, 4, 2]], [1, [40, 24, 15, 12, 5, 4, 3]], [1, [35, 30, 14, 12, 5, 4, 3]], [1, [35, 20, 15, 14, 12, 5, 2]], [1, [28, 21, 20, 18, 9, 5, 2]]]]
[104, [[1, [48, 18, 16, 9, 6, 4, 3]], [1, [42, 28, 21, 7, 4, 2]], [1, [35, 24, 15, 14, 8, 6, 2]], [1, [30, 28, 21, 20, 3, 2]], [1, [30, 28, 14, 10, 7, 6, 5, 4]], [1, [28, 20, 18, 14, 9, 7, 5, 3]]]]
[105, [[1, [42, 30, 20, 7, 4, 2]], [1, [40, 20, 12, 10, 8, 6, 5, 4]], [1, [40, 18, 15, 9, 8, 6, 5, 4]], [1, [33, 22, 20, 12, 11, 5, 2]]]]
[106, [[1, [45, 36, 12, 6, 5, 2]], [1, [45, 15, 12, 10, 9, 6, 5, 4]], [1, [40, 30, 15, 8, 6, 4, 3]], [1, [40, 24, 20, 10, 5, 4, 3]], [1, [40, 18, 12, 10, 9, 8, 6, 3]], [1, [36, 30, 18, 10, 5, 4, 3]], [1, [36, 24, 18, 12, 8, 6, 2]], [1, [36, 20, 18, 15, 10, 5, 2]], [1, [33, 24, 22, 11, 8, 6, 2]], [1, [24, 18, 15, 12, 10, 9, 8, 6, 4]]]]
[107, [[1, [30, 28, 20, 14, 7, 6, 2]], [1, [30, 24, 18, 10, 9, 8, 5, 3]]]]
[108, [[1, [60, 30, 6, 5, 4, 3]], [1, [60, 20, 15, 6, 5, 2]], [1, [60, 20, 12, 10, 4, 2]], [1, [60, 18, 15, 9, 4, 2]], [1, [54, 27, 12, 9, 4, 2]], [1, [48, 20, 16, 12, 5, 4, 3]], [1, [42, 24, 15, 10, 8, 7, 2]], [1, [36, 28, 21, 18, 3, 2]], [1, [30, 28, 21, 12, 10, 5, 2]], [1, [28, 24, 21, 20, 8, 5, 2]], [1, [28, 21, 20, 15, 10, 6, 5, 3]], [1, [28, 21, 18, 15, 10, 9, 4, 3]]]]
[109, [[1, [72, 12, 9, 8, 6, 2]], [1, [70, 28, 5, 4, 2]], [1, [48, 24, 16, 8, 6, 4, 3]], [1, [48, 16, 15, 12, 10, 6, 2]], [1, [45, 30, 12, 9, 6, 4, 3]], [1, [45, 20, 15, 12, 9, 6, 2]], [1, [42, 36, 18, 7, 4, 2]], [1, [42, 20, 15, 10, 7, 6, 5, 4]], [1, [40, 28, 14, 10, 8, 7, 2]], [1, [40, 24, 18, 10, 9, 6, 2]], [1, [36, 30, 20, 18, 3, 2]], [1, [30, 28, 14, 12, 10, 7, 5, 3]], [1, [30, 20, 18, 15, 10, 9, 4, 3]], [1, [28, 24, 20, 14, 8, 7, 5, 3]]]]
[110, [[1, [84, 14, 6, 4, 2]], [1, [72, 24, 9, 3, 2]], [1, [45, 42, 9, 7, 5, 2]], [1, [42, 24, 18, 9, 8, 7, 2]], [1, [42, 18, 15, 10, 9, 7, 6, 3]], [1, [40, 35, 14, 8, 6, 4, 3]], [1, [40, 18, 15, 12, 9, 8, 5, 3]], [1, [35, 20, 15, 14, 12, 6, 5, 3]], [1, [35, 18, 15, 14, 12, 9, 4, 3]], [1, [33, 22, 15, 12, 11, 10, 4, 3]], [1, [28, 21, 20, 18, 9, 6, 5, 3]]]]
[111, [[1, [56, 42, 8, 3, 2]], [1, [56, 21, 12, 8, 7, 4, 3]], [1, [48, 18, 16, 12, 9, 6, 2]], [1, [42, 28, 21, 7, 6, 4, 3]], [1, [42, 20, 18, 9, 7, 6, 5, 4]], [1, [36, 28, 18, 14, 7, 6, 2]], [1, [35, 30, 15, 14, 10, 5, 2]], [1, [28, 18, 15, 14, 10, 9, 7, 6, 4]]]]
[112, [[1, [56, 28, 14, 8, 4, 2]], [1, [42, 30, 20, 7, 6, 4, 3]], [1, [33, 22, 20, 12, 11, 6, 5, 3]], [1, [33, 22, 18, 12, 11, 9, 4, 3]]]]
[113, [[1, [60, 40, 8, 3, 2]], [1, [60, 24, 15, 8, 4, 2]], [1, [45, 24, 12, 9, 8, 6, 5, 4]], [1, [40, 30, 15, 12, 8, 6, 2]], [1, [40, 24, 20, 12, 10, 5, 2]], [1, [40, 24, 18, 15, 9, 5, 2]], [1, [40, 20, 18, 10, 9, 8, 5, 3]], [1, [36, 30, 18, 12, 10, 5, 2]], [1, [36, 24, 20, 18, 8, 5, 2]], [1, [36, 20, 18, 15, 10, 6, 5, 3]], [1, [35, 30, 18, 14, 9, 5, 2]], [1, [35, 20, 18, 14, 10, 9, 4, 3]], [1, [33, 30, 22, 11, 10, 5, 2]], [1, [28, 24, 21, 15, 10, 8, 4, 3]], [1, [24, 20, 18, 15, 10, 9, 8, 5, 4]]]]
[114, [[1, [56, 24, 21, 7, 4, 2]], [1, [42, 40, 10, 8, 7, 4, 3]], [1, [42, 20, 15, 12, 10, 7, 5, 3]], [1, [40, 30, 24, 15, 3, 2]], [1, [30, 24, 20, 15, 10, 8, 4, 3]]]]
[115, [[1, [84, 14, 12, 3, 2]], [1, [60, 30, 12, 6, 5, 2]], [1, [60, 20, 12, 10, 6, 4, 3]], [1, [60, 18, 15, 9, 6, 4, 3]], [1, [54, 27, 12, 9, 6, 4, 3]], [1, [45, 28, 21, 9, 5, 4, 3]], [1, [42, 24, 15, 10, 8, 7, 6, 3]], [1, [40, 28, 21, 10, 8, 6, 2]], [1, [35, 24, 15, 14, 12, 8, 4, 3]], [1, [30, 28, 21, 12, 10, 6, 5, 3]], [1, [28, 24, 21, 20, 8, 6, 5, 3]], [1, [28, 24, 21, 18, 9, 8, 4, 3]], [1, [28, 21, 18, 15, 12, 10, 9, 2]], [1, [28, 20, 15, 14, 12, 10, 7, 5, 4]]]]
[116, [[1, [72, 20, 9, 8, 5, 2]], [1, [70, 28, 6, 5, 4, 3]], [1, [48, 30, 16, 10, 5, 4, 3]], [1, [48, 24, 16, 12, 8, 6, 2]], [1, [48, 20, 16, 15, 10, 5, 2]], [1, [45, 30, 20, 9, 5, 4, 3]], [1, [42, 36, 18, 7, 6, 4, 3]], [1, [42, 30, 12, 10, 7, 6, 5, 4]], [1, [42, 24, 20, 8, 7, 6, 5, 4]], [1, [42, 20, 18, 12, 9, 7, 5, 3]], [1, [40, 30, 20, 10, 8, 6, 2]], [1, [40, 28, 14, 10, 8, 7, 6, 3]], [1, [30, 24, 20, 18, 9, 8, 4, 3]], [1, [30, 20, 18, 15, 12, 10, 9, 2]], [1, [28, 24, 15, 14, 10, 8, 7, 6, 4]], [1, [28, 18, 15, 14, 12, 10, 9, 7, 3]]]]
[117, [[1, [45, 42, 9, 7, 6, 5, 3]], [1, [45, 30, 15, 10, 9, 6, 2]], [1, [42, 24, 18, 9, 8, 7, 6, 3]], [1, [40, 35, 14, 12, 8, 6, 2]], [1, [33, 24, 22, 12, 11, 8, 4, 3]], [1, [30, 28, 21, 20, 12, 4, 2]], [1, [28, 20, 18, 14, 12, 9, 7, 5, 4]]]]
[118, [[1, [70, 21, 14, 6, 5, 2]], [1, [48, 28, 21, 16, 3, 2]], [1, [48, 20, 18, 16, 9, 5, 2]], [1, [45, 36, 15, 10, 5, 4, 3]], [1, [45, 28, 14, 9, 7, 6, 5, 4]], [1, [42, 35, 21, 15, 3, 2]], [1, [42, 28, 21, 12, 7, 6, 2]], [1, [40, 35, 24, 14, 3, 2]], [1, [36, 24, 18, 15, 10, 8, 4, 3]], [1, [35, 30, 24, 14, 8, 5, 2]], [1, [35, 30, 15, 14, 10, 6, 5, 3]], [1, [35, 24, 20, 14, 10, 8, 4, 3]], [1, [30, 28, 20, 14, 12, 7, 4, 3]], [1, [28, 24, 18, 14, 9, 8, 7, 6, 4]]]]
[119, [[1, [60, 20, 15, 12, 5, 4, 3]], [1, [56, 28, 14, 8, 6, 4, 3]], [1, [56, 21, 15, 10, 8, 7, 2]], [1, [48, 42, 16, 7, 4, 2]], [1, [48, 30, 20, 16, 3, 2]], [1, [45, 24, 15, 10, 9, 8, 5, 3]], [1, [42, 30, 20, 12, 7, 6, 2]], [1, [40, 28, 21, 15, 8, 5, 2]], [1, [35, 28, 21, 15, 14, 4, 2]]]]
[120, [[1, [60, 24, 15, 8, 6, 4, 3]], [1, [45, 36, 18, 9, 5, 4, 3]], [1, [40, 36, 18, 10, 8, 6, 2]], [1, [40, 30, 20, 15, 8, 5, 2]], [1, [40, 28, 15, 14, 8, 7, 5, 3]], [1, [40, 24, 20, 12, 10, 6, 5, 3]], [1, [40, 24, 18, 15, 9, 6, 5, 3]], [1, [40, 24, 18, 12, 10, 9, 4, 3]], [1, [36, 30, 18, 12, 10, 6, 5, 3]], [1, [36, 24, 20, 18, 8, 6, 5, 3]], [1, [35, 30, 20, 15, 14, 4, 2]], [1, [35, 30, 18, 14, 9, 6, 5, 3]], [1, [35, 20, 18, 14, 12, 10, 9, 2]], [1, [33, 30, 22, 11, 10, 6, 5, 3]], [1, [33, 22, 18, 15, 11, 10, 9, 2]], [1, [30, 24, 18, 12, 10, 9, 8, 5, 4]], [1, [28, 24, 21, 15, 12, 10, 8, 2]]]]
[121, [[1, [80, 16, 10, 8, 5, 2]], [1, [72, 36, 8, 3, 2]], [1, [72, 15, 10, 9, 8, 4, 3]], [1, [56, 24, 21, 7, 6, 4, 3]], [1, [56, 21, 18, 9, 8, 7, 2]], [1, [48, 28, 16, 14, 7, 6, 2]], [1, [45, 36, 20, 15, 3, 2]], [1, [45, 35, 14, 10, 9, 6, 2]], [1, [42, 40, 12, 10, 8, 7, 2]], [1, [42, 35, 15, 14, 7, 6, 2]], [1, [42, 24, 20, 12, 8, 7, 5, 3]], [1, [36, 28, 21, 18, 12, 4, 2]], [1, [33, 28, 22, 21, 11, 4, 2]], [1, [30, 24, 20, 15, 12, 10, 8, 2]], [1, [28, 24, 15, 14, 12, 10, 8, 7, 3]], [1, [28, 21, 20, 15, 12, 10, 6, 5, 4]]]]
[122, [[1, [63, 28, 18, 7, 4, 2]], [1, [60, 18, 15, 12, 9, 6, 2]], [1, [54, 27, 20, 9, 5, 4, 3]], [1, [45, 28, 21, 12, 9, 5, 2]], [1, [36, 30, 20, 18, 12, 4, 2]], [1, [36, 28, 18, 14, 12, 7, 4, 3]], [1, [33, 30, 22, 20, 11, 4, 2]], [1, [33, 28, 22, 14, 11, 7, 4, 3]], [1, [28, 24, 21, 18, 12, 9, 8, 2]], [1, [28, 24, 20, 14, 12, 8, 7, 5, 4]], [1, [28, 21, 18, 15, 12, 10, 9, 6, 3]]]]
[123, [[1, [90, 18, 10, 3, 2]], [1, [72, 24, 12, 9, 4, 2]], [1, [72, 20, 9, 8, 6, 5, 3]], [1, [70, 28, 12, 6, 5, 2]], [1, [54, 27, 15, 10, 9, 6, 2]], [1, [48, 36, 18, 16, 3, 2]], [1, [48, 30, 16, 12, 10, 5, 2]], [1, [48, 24, 20, 16, 8, 5, 2]], [1, [48, 20, 16, 15, 10, 6, 5, 3]], [1, [48, 18, 16, 15, 10, 9, 4, 3]], [1, [45, 36, 30, 6, 4, 2]], [1, [45, 30, 20, 12, 9, 5, 2]], [1, [45, 28, 14, 12, 9, 7, 5, 3]], [1, [42, 36, 18, 12, 7, 6, 2]], [1, [42, 33, 22, 11, 7, 6, 2]], [1, [42, 18, 15, 12, 10, 9, 7, 6, 4]], [1, [30, 24, 20, 18, 12, 9, 8, 2]], [1, [30, 20, 18, 15, 12, 10, 9, 6, 3]], [1, [28, 24, 18, 14, 12, 9, 8, 7, 3]], [1, [28, 21, 20, 18, 12, 9, 6, 5, 4]]]]
[124, [[1, [56, 42, 12, 8, 4, 2]], [1, [45, 30, 24, 9, 8, 6, 2]], [1, [42, 30, 18, 10, 9, 7, 5, 3]], [1, [40, 36, 18, 15, 8, 5, 2]], [1, [40, 35, 20, 14, 8, 5, 2]], [1, [36, 35, 18, 15, 14, 4, 2]], [1, [30, 28, 21, 20, 12, 6, 4, 3]], [2, [24, 20, 18, 15, 10, 9, 8, 6, 5, 4, 3, 2]]]]
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