Hurwitz Zeta Rational Sequence showing primes in the denominator
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From: GHMM on 1 Jun 2010 04:22 I've been looking at a zeta function to produce the primes and have come up with the following: Table[D[FindSequenceFunction[Table[Rationalize[ i^m N[Zeta[1 - m, (-i - 1)/i] + Zeta[1 - m, -(1/i)], 80]], {i, 80}] , n],{n, m}], {m, 30}] output : 2, 5/3, 6, 122/5, 120, 5000/7, 5040, 40656, 362880, 39312000/11, 39916800, 6489711360/13, 6227020800, 72648576000, 1307674368000, 671011307366400/17, 355687428096000, -(621352061890560000/19), 121645100408832000, 131163645205064908800, 51090942171709440000, - (14526772739252431257600000/23)... Can someone please help to fit the numerators of this rational sequence into a product, the denominators are the primes. Ray
From: Peter Breitfeld on 1 Jun 2010 07:47 GHMM wrote: > I've been looking at a zeta function to produce the primes and have > come up with the following: > > Table[D[FindSequenceFunction[Table[Rationalize[ i^m N[Zeta[1 - m, (-i > - 1)/i] + Zeta[1 - m, -(1/i)], 80]], {i, 80}] , n],{n, m}], {m, 30}] > > output : > > 2, 5/3, 6, 122/5, 120, 5000/7, 5040, 40656, 362880, 39312000/11, > 39916800, 6489711360/13, 6227020800, 72648576000, 1307674368000, > 671011307366400/17, 355687428096000, -(621352061890560000/19), > 121645100408832000, 131163645205064908800, 51090942171709440000, - > (14526772739252431257600000/23)... > > Can someone please help to fit the numerators of this rational > sequence into a product, the denominators are the primes. > > Ray > Suppose your table is tt. Then define: schoen[{x_,y_}]:=HoldForm[x^y] zerlege[expr_Integer] := Times @@ schoen /@ FactorInteger[expr] zerlege[expr_Rational] := zerlege[Numerator[expr]]/Denominator[expr] and do zerlege/@tt It seams, that I needed the HoldForm to prevent Mathematica from automatically calculate the Numerator into the original number. //Peter -- _________________________________________________________________ Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de
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