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 A166642 #15 Feb 06 2025 08:22:55
%S A166642 1,6,8,36,12,48,16,216,64,72,24,288,28,96,96,1296,36,384,40,432,128,
%T A166642 144,48,1728,144,168,512,576,60,576,64,7776,192,216,192,2304,76,240,
%U A166642 224,2592,84,768,88,864,768,288,96,10368,256,864
%N A166642 Totally multiplicative sequence with a(p) = 2*(p+1) for prime p.
%H A166642 G. C. Greubel, <a href="/A166642/b166642.txt">Table of n, a(n) for n = 1..10000</a>
%F A166642 Multiplicative with a(p^e) = (2*(p+1))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(p(k)+1))^e(k).
%F A166642 a(n) = A061142(n) * A003959(n) = 2^bigomega(n) * A003959(n) = 2^A001222(n) * A003959(n).
%t A166642 a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 1)^fi[[All, 2]])); Table[a[n]*2^(PrimeOmega[n]), {n, 1, 100}] (* _G. C. Greubel_, May 20 2016 *)
%t A166642 f[p_, e_] := (2*(p+1))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 18 2023 *)
%Y A166642 Cf. A001222, A003959, A061142.
%K A166642 nonn,easy,mult
%O A166642 1,2
%A A166642 _Jaroslav Krizek_, Oct 18 2009