A123476 - OEIS

%I #10 Jul 11 2018 04:38:11

%S 1,4,18,72,450,2700,22050,176400,1587600,15876000,192099600,

%T 2305195200,32464832400,454507653600,6817614804000,109081836864000,

%U 1970290678356000,35465232210408000,711274934886516000

%N a(n) = (n!)^2/phi(n!), where phi is Euler's totient function.

%C a(n) is a solution to the equation phi(x) = n!.

%H T. D. Noe, <a href="/A123476/b123476.txt">Table of n, a(n) for n=1..100</a>

%H P. Erdos and J. Lambek, <a href="https://www.jstor.org/stable/2305755">Problem 4221</a>, Amer. Math. Monthly, 55 (1948), 103.

%t Table[(n!)^2/EulerPhi[n!],{n,20}] (* _Harvey P. Dale_, Nov 29 2015 *)

%o (PARI) a(n) = (n!)^2/eulerphi(n!); \\ _Michel Marcus_, Jul 11 2018

%Y Cf. A000010, A000142, A002202 (values taken by phi(x)).

%Y Cf. A055487 (least m such that phi(m) = n!).

%K nonn

%O 1,2

%A _T. D. Noe_, Sep 27 2006