%I #7 Sep 08 2022 08:45:06
%S 1,8,216,864,108000,12000,4116000,16464000,1333584000,1333584000,
%T 1775000304000,1775000304000,3899675667888000,3899675667888000,
%U 3899675667888000,15598702671552000,76636426225334976000,2838386156493888000,19468490647391577792000,19468490647391577792000
%N Denominator of Sum_{k=1..n} phi(k)/k^3.
%H G. C. Greubel, <a href="/A072159/b072159.txt">Table of n, a(n) for n = 1..770</a>
%e 1, 9/8, 259/216, 1063/864, 136331/108000, 15259/12000, ...
%p with(numtheory); seq(denom(add(phi(k)/k^3, k = 1..n)), n = 1..25); # _G. C. Greubel_, Aug 26 2019
%t Table[Denominator[Sum[EulerPhi[k]/k^3, {k, n}]], {n, 25}] (* _G. C. Greubel_, Aug 26 2019 *)
%o (PARI) a(n) = denominator( sum(k=1, n, eulerphi(k)/k^3)); \\ _G. C. Greubel_, Aug 26 2019
%o (Magma) [Denominator( &+[EulerPhi(k)/k^3: k in [1..n]] ): n in [1..25]]; // _G. C. Greubel_, Aug 26 2019
%o (Sage) [denominator( sum(euler_phi(k)/k^3 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^3) ) ); # _G. C. Greubel_, Aug 26 2019
%Y Cf. A072158.
%K nonn,frac
%O 1,2
%A _N. J. A. Sloane_, Jun 28 2002