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 A343517 #23 May 23 2021 08:48:04
%S A343517 1,4,12,42,130,506,1722,6622,24426,93427,352726,1359388,5200312,
%T A343517 20097156,77567064,300787366,1166803126,4539197723,17672631918,
%U A343517 68933307843,269129530770,1052113994340,4116715363822,16124224571368,63205303313900,247961973949536
%N A343517 a(n) = Sum_{1 <= x_1 <= x_2 <= ... <= x_n <= n} gcd(x_1, x_2, ... , x_n, n).
%H A343517 Vaclav Kotesovec, <a href="/A343517/b343517.txt">Table of n, a(n) for n = 1..1650</a>
%F A343517 a(n) = Sum_{d|n} phi(n/d) * binomial(d+n-1, n).
%F A343517 a(n) = [x^n] Sum_{k >= 1} phi(k) * x^k/(1 - x^k)^(n+1).
%F A343517 a(n) ~ 2^(2*n - 1) / sqrt(Pi*n). - _Vaclav Kotesovec_, May 23 2021
%t A343517 a[n_] := DivisorSum[n, EulerPhi[n/#] * Binomial[n + # - 1, n] &]; Array[a, 25] (* _Amiram Eldar_, Apr 18 2021 *)
%o A343517 (PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*binomial(d+n-1, n));
%Y A343517 Main diagonal of A343516.
%Y A343517 Cf. A000010, A156834, A332508, A332517.
%K A343517 nonn
%O A343517 1,2
%A A343517 _Seiichi Manyama_, Apr 17 2021