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 A143268 #14 Nov 27 2024 07:25:18
%S A143268 1,3,12,20,60,42,168,144,270,220,660,312,1092,630,960,1088,2448,1026,
%T A143268 3420,1680,2772,2530,6072,2400,6500,4212,6804,4872,12180,3720,14880,
%U A143268 8448,11220,9520,15120,7992,25308,13338,18720,13120,34440,10836,39732
%N A143268 a(n) = phi(n)*T(n), where phi(n) is Euler's totient function (A000010) and T(n) = n*(n+1)/2 is the n-th triangular number (A000217).
%F A143268 a(n) = sum of n-th row of triangle A143267.
%F A143268 a(n) = n*(n+1)*phi(n)/2. - _Emeric Deutsch_, Aug 23 2008
%F A143268 Sum_{k=1..n} a(k) ~ c * n^4, where c = 3/(4*Pi^2) = A323669 / 10 = 0.0759908... . - _Amiram Eldar_, Nov 27 2024
%e A143268 a(4) = 20 = phi(4) * T(4) = 2 * 10.
%e A143268 a(4) = 20 = sum of row 4 terms of triangle A143267: (2 + 4 + 6 + 8).
%p A143268 with(numtheory): seq((1/2)*n*(n+1)*phi(n),n=1..45); # _Emeric Deutsch_, Aug 23 2008
%o A143268 (PARI) a(n)=eulerphi(n)*n*(n+1)/2 \\ _Charles R Greathouse IV_, Mar 05 2013
%Y A143268 Cf. A000010, A000217, A143267, A323669.
%K A143268 nonn
%O A143268 1,2
%A A143268 _Gary W. Adamson_, Aug 03 2008
%E A143268 Extended by _Emeric Deutsch_, Aug 16 2008