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 A333576 #10 Sep 21 2024 08:42:31
%S A333576 1,1,3,6,10,6,21,28,36,20,55,36,78,42,60,120,136,72,171,120,126,110,
%T A333576 253,168,300,156,351,252,406,120,465,496,330,272,420,432,666,342,468,
%U A333576 560,820,252,903,660,720,506,1081,720,1176,600,816,936,1378,702,1100,1176,1026,812,1711,720
%N A333576 a(1) = 1; thereafter a(n) = n * uphi(n) / 2.
%C A333576 The unitary version of A023896.
%F A333576 a(n) = (n/2) * Sum_{d|n, gcd(d, n/d) = 1} (-1)^omega(n/d) * (d + 1).
%F A333576 Sum_{k=1..n} a(k) ~ c * n^3, where c = (Pi^2/36) * Product_{p prime} (1 - (2*p-1)/p^3) = A353908 * A065464 = 0.117407... . - _Amiram Eldar_, Sep 21 2024
%t A333576 uphi[n_] := Times @@ (#[[1]]^#[[2]] - 1 & /@ FactorInteger[n]); a[1] = 1; a[n_] := n uphi[n]/2; Table[a[n], {n, 1, 60}]
%t A333576 a[n_] := (n/2) Sum[If[GCD[d, n/d] == 1, (-1)^PrimeNu[n/d] (d + 1), 0], {d, Divisors[n]}]; Table[a[n], {n, 1, 60}]
%o A333576 (PARI) a(n) = if(n == 1, 1, my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^f[i, 2] - 1) * n / 2); \\ _Amiram Eldar_, Sep 21 2024
%Y A333576 Cf. A001221, A023896, A047994, A065464, A076479, A145388, A353908.
%K A333576 nonn,easy
%O A333576 1,3
%A A333576 _Ilya Gutkovskiy_, Mar 27 2020