(*https://jmorken.github.io/20210505%20tree%20of%20composites/tree%\
20of%20composites%20page4%20-%20additional%20proportions.htm*)

Print["test to see how rare the a,b,c,d,e values are (there are \
multiple solutions to the equation)"]

2927/2310 == (480/2310)*0 + (968/2310)*1 + (652/2310)*2 + (186/
     2310)*3 + (23/2310)*4 + (1/2310)*5 == 1/2 + 1/3 + 1/5 + 1/7 + 1/11

p1 = 2;
p2 = 3;
p3 = 5;
p4 = 7;
p5 = 11;
x = p1*p2*p3*p4*p5;
y = 1/p1 + 1/p2 + 1/p3 + 1/p4 + 1/p5;
a = 480;
b = 968;
c = 652;
d = 186;
e = 23;
f = 1;

2927/x == (a/x)*0 + (b/x)*1 + (c/x)*2 + (d/x)*3 + (e/x)*4 + (f/
     x)*5 == y

trueListabcdef = {};
trueSumXCount = 0;
trueCount = 0;
falseCount = 0;
For[a = 470, a < 490, a++,
 For[b = 960, b < 970, b++,
  For[c = 650, c < 660, c++,
   For[d = 180, d < 190, d++,
    For[e = 10, e < 30, e++,
     For[f = 0, f < 20, f++,
      If[x == a + b + c + d + e + f,
       trueSumXCount = trueSumXCount + 1;
       If[
        2927/x == (a/x)*0 + (b/x)*1 + (c/x)*2 + (d/x)*3 + (e/
             x)*4 + (f/x)*5 == y,
        (*Print[{a,b,c,d,e,f}]*)
        AppendTo[trueListabcdef, {a, b, c, d, e, f}];
        trueCount = trueCount + 1
        ],
       falseCount = falseCount + 1
       ]
      ]
     ]
    ]
   ]
  ]
 ]
trueSumXCount
trueCount
falseCount
N[trueCount/falseCount]
N[falseCount/trueCount]
Length[trueListabcdef]
Take[trueListabcdef, 10]


(* some other abcdef \
solutions:{{475,969,659,188,19,0},{475,969,659,189,17,1},{476,968,658,\
189,19,0},{476,968,659,187,20,0},{476,968,659,188,18,1},{476,968,659,\
189,16,2},{476,969,657,188,20,0},{476,969,657,189,18,1},{476,969,658,\
186,21,0},{476,969,658,187,19,1}}*)