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 A334664 #18 Mar 30 2024 15:07:08
%S A334664 1,2,1,2,1,4,1,8,3,4,1,24,1,4,1,8,1,72,1,8,1,4,1,768,1,4,3,8,1,16,1,
%T A334664 16,1,4,1,3888,1,4,1,256,1,16,1,8,9,4,1,1536,1,8,1,8,1,144,1,256,1,4,
%U A334664 1,2304,1,4,9,16,1,16,1,8,1,16,1,1492992,1,4,3,8,1
%N A334664 a(n) = Product_{d|n} gcd(d, tau(d)).
%H A334664 Antti Karttunen, <a href="/A334664/b334664.txt">Table of n, a(n) for n = 1..10000</a>
%F A334664 a(p) = 1 for p = odd primes (A065091).
%e A334664 a(6) = gcd(1, tau(1)) * gcd(2, tau(2)) * gcd(3, tau(3)) * gcd(6, tau(6)) = gcd(1, 1) * gcd(2, 2) * gcd(3, 2) * gcd(6, 4) = 1 * 2 * 1 * 2 = 4.
%t A334664 Table[Times@@GCD[Divisors[n],DivisorSigma[0,Divisors[n]]],{n,80}] (* _Harvey P. Dale_, Mar 30 2024 *)
%o A334664 (Magma) [&*[GCD(d, #Divisors(d)): d in Divisors(n)]: n in [1..100]]
%o A334664 (PARI) a(n) = my(d=divisors(n)); prod(k=1, #d, gcd(d[k], numdiv(d[k]))); \\ _Michel Marcus_, May 08-11 2020
%Y A334664 Cf. A322979 (Sum_{d|n} gcd(d, tau(d))), A334491 (Product_{d|n} gcd(d, sigma(d))).
%Y A334664 Cf. A000005 (tau(n)), A000203 (sigma(n)), A009191 (gcd(n, tau(n))).
%K A334664 nonn
%O A334664 1,2
%A A334664 _Jaroslav Krizek_, May 07 2020