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 A065093 #22 Jul 13 2024 02:22:57
%S A065093 1,2,5,8,16,20,36,44,68,76,120,124,188,196,276,272,404,380,544,532,
%T A065093 716,668,968,860,1184,1120,1472,1332,1896,1624,2204,2036,2656,2352,
%U A065093 3284,2752,3684,3356,4324,3744,5192,4312,5720,5180,6540,5628,7768,6388,8476
%N A065093 Convolution of A000010 with itself.
%H A065093 Vaclav Kotesovec, <a href="/A065093/b065093.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harry J. Smith)
%H A065093 A. E. Ingham, <a href="https://doi.org/10.1112/jlms/s1-2.3.202">Some asymptotic formulae in the theory of numbers</a>, Journal of the London Mathematical Society, Vol. s1-2, No. 3 (1927), pp. 202-208.
%F A065093 a(n) = Sum_{k=1..n} phi(k)*phi(n+1-k), where phi is Euler totient function (A000010).
%F A065093 G.f.: (1/x)*(Sum_{k>=1} mu(k)*x^k/(1 - x^k)^2)^2. - _Ilya Gutkovskiy_, Jan 31 2017
%F A065093 a(n) ~ (n^3/6) * c * Product_{primes p|n+1} ((p^3-2*p+1)/(p*(p^2-2))), where c = Product_{p prime} (1 - 2/p^2) = 0.322634... (A065474) (Ingham, 1927). - _Amiram Eldar_, Jul 13 2024
%t A065093 Table[Sum[EulerPhi[j]*EulerPhi[n-j], {j, 1, n-1}], {n, 2, 50}] (* _Vaclav Kotesovec_, Aug 18 2021 *)
%o A065093 (PARI) { for (n=1, 1000, a=sum(k=1, n, eulerphi(k)*eulerphi(n+1-k)); write("b065093.txt", n, " ", a) ) } \\ _Harry J. Smith_, Oct 06 2009
%Y A065093 Cf. A000010, A000385, A055507, A065474, A330319.
%Y A065093 Column k=2 of A340995.
%K A065093 easy,nonn
%O A065093 1,2
%A A065093 _Vladeta Jovovic_, Nov 11 2001