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I am completely new to Mathematica and I need some help (sorry if it is trivial, but I haven't found the answer). I have this code

K[Q_, n_Integer] := 
  Module[{z, x},
    SymmetricReduction[
      SeriesCoefficient[
        Product[
          ComposeSeries[Series[Q[z], {z, 0, n}], Series[x[i] z, {z, 0, n}]], 
          {i, 1, n}], 
        n], 
      Table[x[i], {i, 1, n}], 
      Table[Subscript[c, i], {i, 1, n}]][[1]]]

Then I evaluate

K[Sqrt[#]/Tanh[Sqrt[#]]&, 8] /. c -> p

The output is a polynomial in p1, p2 ... p8 (in this case) with coefficients written as fractions (23412/7538293, for example). What should I do in order to output the numerator and denominator of each function in it's prime factorization (preferably factor out the common divisor of the denominator)?

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  • $\begingroup$ Together will pull out the lcm of the denominators. I'm not sure if that's quite what you want though. $\endgroup$ – Daniel Lichtblau Mar 3 '18 at 15:50
  • $\begingroup$ @DanielLichtblau Thank you for this. Is there a way to write the denominator and numerator of each fraction (after the pulling out of lcm) as product of prime numbers (prime factorization)? $\endgroup$ – Silviu Mar 3 '18 at 18:25
  • $\begingroup$ The method by @BIll looks viable for this. $\endgroup$ – Daniel Lichtblau Mar 3 '18 at 19:52

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