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 A029940 #31 Jul 08 2025 19:26:15
%S A029940 1,1,2,2,4,4,6,8,12,16,10,32,12,36,64,64,16,144,18,256,144,100,22,
%T A029940 1024,80,144,216,864,28,4096,30,1024,400,256,576,13824,36,324,576,
%U A029940 16384,40,20736,42,4000,9216,484,46,131072,252,6400,1024,6912,52,46656,1600
%N A029940 a(n) = Product_{d|n} phi(d).
%H A029940 T. D. Noe, <a href="/A029940/b029940.txt">Table of n, a(n) for n = 1..1000</a>
%H A029940 J. R. Collis, <a href="https://www.jstor.org/stable/24496802">On products of multiplicative functions</a>, The Mathematical Gazette, Vol. 97, No. 539 (2013), pp. 263-264.
%F A029940 If n = Product_{i} p_i^e_i then a(n) = (sqrt(n) * Product_{i} (1 - 1/p_i)^(e_i/(e_i + 1))) ^ d(n), where d(n) is the number of divisors of n (Collis, 2013). - _Amiram Eldar_, Jun 16 2020
%F A029940 a(n) = Product_{k=1..n} phi(gcd(n,k))^(1/phi(n/gcd(n,k))) = Product_{k=1..n} phi(n/gcd(n,k))^(1/phi(n/gcd(n,k))). - _Richard L. Ollerton_, Nov 07 2021
%p A029940 seq(mul(numtheory:-phi(i),i=numtheory:-divisors(n)), n=1..100); # _Robert Israel_, Nov 21 2014
%t A029940 Table[Product[EulerPhi[i], {i, Divisors[n]}], {n, 100}] (* _Carl Najafi_, Sep 06 2011 *)
%o A029940 (PARI) a(n) = my(d = divisors(n)); prod(k=1, #d, eulerphi(d[k])); \\ _Michel Marcus_, Nov 21 2014
%Y A029940 Cf. A000005, A000010.
%K A029940 nonn
%O A029940 1,3
%A A029940 _N. J. A. Sloane_
%E A029940 More terms from _Carl Najafi_, Sep 06 2011