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 A333557 #15 Apr 30 2023 02:08:53
%S A333557 1,2,4,6,8,8,12,14,16,16,20,24,24,24,32,30,32,32,36,48,48,40,44,56,48,
%T A333557 48,52,72,56,64,60,62,80,64,96,96,72,72,96,112,80,96,84,120,128,88,92,
%U A333557 120,96,96,128,144,104,104,160,168,144,112,116,192,120,120,192,126,192,160,132,192,176,192
%N A333557 a(n) = Sum_{d|n, gcd(d, n/d) = 1} uphi(d) * uphi(n/d), where uphi = unitary totient function (A047994).
%H A333557 Amiram Eldar, <a href="/A333557/b333557.txt">Table of n, a(n) for n = 1..10000</a>
%F A333557 If n = Product (p_j^k_j) then a(n) = Product (2 * (p_j^k_j - 1)).
%F A333557 a(n) = 2^omega(n) * uphi(n).
%F A333557 a(n) = Sum_{d|n, gcd(d, n/d) = 1} (-2)^omega(n/d) * 2^omega(d) * d.
%F A333557 a(n) = Sum_{d|n, gcd(d, n/d) = 1} (-1)^omega(n/d) * A145388(d).
%t A333557 uphi[1] = 1; uphi[n_] := Times @@ (#[[1]]^#[[2]] - 1 & /@ FactorInteger[n]); a[n_] := Sum[If[GCD[d, n/d] == 1, uphi[d] uphi[n/d], 0], {d, Divisors[n]}]; Table[a[n], {n, 1, 70}]
%t A333557 Table[Sum[If[GCD[d, n/d] == 1, (-2)^PrimeNu[n/d] 2^PrimeNu[d] d, 0], {d, Divisors[n]}], {n, 1, 70}]
%t A333557 f[p_, e_] := 2*(p^e-1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Apr 30 2023 *)
%o A333557 (PARI) a(n) = sumdiv(n, d, if (gcd(d, n/d) == 1, (-2)^omega(n/d)*2^omega(d)*d)); \\ _Michel Marcus_, Mar 27 2020
%Y A333557 Cf. A001221, A029935, A034444, A047994, A055653, A062355, A145388.
%K A333557 nonn,mult
%O A333557 1,2
%A A333557 _Ilya Gutkovskiy_, Mar 26 2020