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 A166634 #21 Feb 05 2025 07:51:31
%S A166634 1,4,8,16,16,32,24,64,64,64,40,128,48,96,128,256,64,256,72,256,192,
%T A166634 160,88,512,256,192,512,384,112,512,120,1024,320,256,384,1024,144,288,
%U A166634 384,1024,160,768,168,640,1024,352,184,2048,576,1024
%N A166634 Totally multiplicative sequence with a(p) = 4*(p-1) for prime p.
%H A166634 G. C. Greubel, <a href="/A166634/b166634.txt">Table of n, a(n) for n = 1..10000</a>
%F A166634 Multiplicative with a(p^e) = (4*(p-1))^e. If n = Product p(k)^e(k) then a(n) = Product (4*(p(k)-1))^e(k).
%F A166634 a(n) = A165825(n) * A003958(n) = 4^bigomega(n) * A003958(n) = 4^A001222(n) * A003958(n).
%t A166634 DirichletInverse[f_][1] = 1/f[1]; DirichletInverse[f_][n_] :=
%t A166634 DirichletInverse[f][n] = -1/f[1]*Sum[f[n/d]*DirichletInverse[f][d], {d, Most[Divisors[n]]}]; muphi[n_] := MoebiusMu[n]*EulerPhi[n]; a[m_] := DirichletInverse[muphi][m]; Table[a[m]*4^(PrimeOmega[m]), {m, 1, 100}] (* _G. C. Greubel_, May 20 2016 *)
%t A166634 f[p_, e_] := (4*(p-1))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 17 2023 *)
%o A166634 (PARI) a(n) = {my(f = factor(n)); for (k=1, #f~, f[k,1] = 4*(f[k,1]-1)); factorback(f);} \\ _Michel Marcus_, May 20 2016
%Y A166634 Cf. A001222, A003958, A165825, A166633.
%K A166634 nonn,easy,mult
%O A166634 1,2
%A A166634 _Jaroslav Krizek_, Oct 18 2009