This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A072158 #13 Dec 28 2024 09:16:16
%S A072158 1,9,259,1063,136331,15259,5305837,21351973,1740485813,1745820149,
%T A072158 2337022458319,2341131255319,5164765371583843,5173292359195843,
%U A072158 5182536034853059,20760610355567611,102246457919648504843,3789825999242633809,26045507479622115279931,26064975970269506857723
%N A072158 Numerator of Sum_{k=1..n} phi(k)/k^3.
%H A072158 G. C. Greubel, <a href="/A072158/b072158.txt">Table of n, a(n) for n = 1..770</a>
%F A072158 Limit_{n->oo} a(n)/A072159(n) = zeta(2)/zeta(3) = 1.368432... (A306633). - _Amiram Eldar_, Dec 28 2024
%e A072158 1, 9/8, 259/216, 1063/864, 136331/108000, 15259/12000, ...
%p A072158 with(numtheory); seq(numer(add(phi(k)/k^3, k = 1..n)), n = 1..25); # _G. C. Greubel_, Aug 26 2019
%t A072158 Numerator[Table[Sum[EulerPhi[k]/k^3,{k,n}],{n,20}]] (* _Harvey P. Dale_, May 27 2012 *)
%t A072158 Numerator[Accumulate[Table[EulerPhi[k]/k^3, {k, 1, 30}]]] (* _Amiram Eldar_, Dec 28 2024 *)
%o A072158 (PARI) a(n) = numerator( sum(k=1, n, eulerphi(k)/k^3)); \\ _G. C. Greubel_, Aug 26 2019
%o A072158 (Magma) [Numerator( &+[EulerPhi(k)/k^3: k in [1..n]] ): n in [1..25]]; // _G. C. Greubel_, Aug 26 2019
%o A072158 (Sage) [numerator( sum(euler_phi(k)/k^3 for k in (1..n)) ) for n in (1..25)] # _G. C. Greubel_, Aug 26 2019
%o A072158 (GAP) List([1..25], n-> NumeratorRat( Sum([1..n], k-> Phi(k)/k^3) ) ); # _G. C. Greubel_, Aug 26 2019
%Y A072158 Cf. A000010, A072159, A306633.
%K A072158 nonn,frac,easy
%O A072158 1,2
%A A072158 _N. J. A. Sloane_, Jun 28 2002