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%I #15 Sep 19 2022 18:55:59
%S 1,4,36,72,1800,1800,88200,176400,529200,105840,12806640,12806640,
%T 2164322160,2164322160,10821610800,21643221600,6254891042400,
%U 6254891042400,2258015666306400,451603133261280,451603133261280,451603133261280,238898057495217120,238898057495217120
%N Denominator of Sum_{k=1..n} phi(k)/k^2.
%H Vincenzo Librandi, <a href="/A072157/b072157.txt">Table of n, a(n) for n = 1..300</a>
%e 1, 5/4, 53/36, 115/72, 3163/1800, 3263/1800, 170687/88200, ...
%p with(numtheory); seq(denom(add(phi(k)/k^2, k = 1..n)), n = 1..25); # _G. C. Greubel_, Aug 26 2019
%t Denominator[Table[Sum[EulerPhi[k]/k^2,{k,n}],{n,30}]] (* _Harvey P. Dale_, Nov 13 2011 *)
%t Accumulate[Table[EulerPhi[n]/n^2,{n,30}]]//Denominator (* More efficient than the first above program. *) (* _Harvey P. Dale_, Sep 19 2022 *)
%o (PARI) a(n) = denominator( sum(k=1, n, eulerphi(k)/k^2)); \\ _G. C. Greubel_, Aug 26 2019
%o (Magma) [Denominator( &+[EulerPhi(k)/k^2: k in [1..n]] ): n in [1..25]]; // _G. C. Greubel_, Aug 26 2019
%o (Sage) [denominator( sum(euler_phi(k)/k^2 for k in (1..n)) ) for n in (1..25)] # _G. C. Greubel_, Aug 26 2019
%o (GAP) List([1..25], n-> DenominatorRat( Sum([1..n], k-> Phi(k)/k^2) ) ); # _G. C. Greubel_, Aug 26 2019
%Y Cf. A072156.
%K nonn,frac
%O 1,2
%A _N. J. A. Sloane_, Jun 28 2002
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