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 A072156 #16 Dec 28 2024 09:16:55
%S A072156 1,5,53,115,3163,3263,170687,352399,1096397,223513,28103473,28459213,
%T A072156 4963286677,5029541437,25532475569,51741301813,15299527769557,
%U A072156 15415359085157,5677532668504877,1144538596366201,1156827116999161,1166157760248361,626832724103131129
%N A072156 Numerator of Sum_{k=1..n} phi(k)/k^2.
%H A072156 Vincenzo Librandi, <a href="/A072156/b072156.txt">Table of n, a(n) for n = 1..300</a>
%F A072156 a(n)/A072157(n) ~ (log(n) + gamma - zeta'(2)/zeta(2)) / zeta(2), where gamma is Euler's constant (A001620). - _Amiram Eldar_, Dec 28 2024
%e A072156 1, 5/4, 53/36, 115/72, 3163/1800, 3263/1800, 170687/88200, ...
%p A072156 with(numtheory); seq(numer(add(phi(k)/k^2, k = 1..n)), n = 1..25); # _G. C. Greubel_, Aug 25 2019
%t A072156 Numerator[Table[Sum[EulerPhi[k]/k^2,{k,n}],{n,30}]] (* _Vincenzo Librandi_, Nov 15 2011 *)
%t A072156 Numerator[Accumulate[Table[EulerPhi[k]/k^2, {k, 1, 30}]]] (* _Amiram Eldar_, Dec 28 2024 *)
%o A072156 (PARI) a(n) = numerator( sum(k=1,n, eulerphi(k)/k^2));
%o A072156 vector(25, n, a(n)) \\ _G. C. Greubel_, Aug 25 2019
%o A072156 (Magma) [Numerator( &+[EulerPhi(k)/k^2: k in [1..n]] ): n in [1..25]]; // _G. C. Greubel_, Aug 25 2019
%o A072156 (Sage) [numerator( sum(euler_phi(k)/k^2 for k in (1..n)) ) for n in (1..25)] # _G. C. Greubel_, Aug 25 2019
%o A072156 (GAP) List([1..25], n-> NumeratorRat( Sum([1..n], k-> Phi(k)/k^2) ) ); # _G. C. Greubel_, Aug 25 2019
%Y A072156 Cf. A000010, A072157.
%Y A072156 Cf. A001620, A013661, A306016.
%K A072156 nonn,frac
%O A072156 1,2
%A A072156 _N. J. A. Sloane_, Jun 28 2002