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%I M3661 #46 Apr 03 2021 22:00:37
%S 1,4,36,144,3600,3600,176400,705600,6350400,1270080,153679680,
%T 153679680,25971865920,25971865920,129859329600,519437318400,
%U 150117385017600,150117385017600,54192375991353600,10838475198270720,221193371393280
%N a(n) = denominator of Sum_{k=1..n} 1/k^2.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Seiichi Manyama, <a href="/A007407/b007407.txt">Table of n, a(n) for n = 1..1152</a> (terms 1..200 from T. D. Noe)
%H D. Y. Savio, E. A. Lamagna and S.-M. Liu, <a href="http://dx.doi.org/10.1007/978-1-4613-9647-5_2">Summation of harmonic numbers</a>, pp. 12-20 of E. Kaltofen and S. M. Watt, editors, Computers and Mathematics, Springer-Verlag, NY, 1989.
%F a(n) = denominator of (Pi^2)/6 - zeta(2, x). - _Artur Jasinski_, Mar 03 2010
%F a(n) = A001044(n) / gcd(A001819(n), A001044(n)). - _Daniel Suteu_, Dec 25 2016
%e 1/1^2 + 1/2^2 + 1/3^2 = 1/1 + 1/4 + 1/9 = 49/36, so a(3) = 36. - _Jon E. Schoenfield_, Dec 26 2014
%p ZL:=n->sum(1/i^2, i=2..n): a:=n->floor(denom(ZL(n))): seq(a(n), n=1..21); # _Zerinvary Lajos_, Mar 28 2007
%t s=0;lst={};Do[s+=n^2/n^4;AppendTo[lst,Denominator[s]],{n,3*4!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jan 24 2009 *)
%t Table[Denominator[Pi^2/6 - Zeta[2, x]], {x, 1, 22}] (* _Artur Jasinski_, Mar 03 2010 *)
%t Denominator[Accumulate[1/Range[30]^2]] (* _Harvey P. Dale_, Nov 08 2012 *)
%o (Haskell)
%o import Data.Ratio ((%), denominator)
%o a007407 n = a007407_list !! (n-1)
%o a007407_list = map denominator $
%o scanl1 (+) $ map (1 %) $ tail a000290_list
%o -- _Reinhard Zumkeller_, Jul 06 2012
%o (PARI) a(n)=denominator(sum(k=1,n,1/k^2)) \\ _Charles R Greathouse IV_, Nov 20 2012
%o (Python)
%o from fractions import Fraction
%o def A007407(n): return sum(Fraction(1,k**2) for k in range(1,n+1)).denominator # _Chai Wah Wu_, Apr 03 2021
%Y Cf. A007406 (numerators), A000290, A035166.
%K nonn,easy,frac,nice
%O 1,2
%A _N. J. A. Sloane_, _Mira Bernstein_
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