%I #29 Nov 27 2021 20:00:22
%S 1,1,2,2,4,4,6,8,12,16,10,32,12,36,64,64,16,144,18,256,144,100,22,
%T 1024,80,144,216,864,28,4096,30,1024,400,256,576,13824,36,324,576,
%U 16384,40,20736,42,4000,9216,484,46,131072,252,6400,1024,6912,52,46656,1600
%N a(n) = Product_{d|n} phi(d).
%H T. D. Noe, <a href="/A029940/b029940.txt">Table of n, a(n) for n = 1..1000</a>
%H 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 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 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 seq(mul(numtheory:-phi(i),i=numtheory:-divisors(n)), n=1..100); # _Robert Israel_, Nov 21 2014
%t Table[Product[EulerPhi[i], {i, Divisors[n]}], {n, 100}] (* _Carl Najafi_, Sep 06 2011 *)
%o (PARI) a(n) = my(d = divisors(n)); prod(k=1, #d, eulerphi(d[k])); \\ _Michel Marcus_, Nov 21 2014
%Y Cf. A000005, A000010.
%K nonn
%O 1,3
%A _N. J. A. Sloane_.
%E More terms from _Carl Najafi_, Sep 06 2011