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%I #11 Aug 07 2020 17:34:47
%S 1,8,32,9216,82944,8294400,1194393600
%N Perfect powers which are totients of factorials.
%C Corresponding values of factorials are 1! (and 2!), 4!, 5!, 8!, 9!, 11! and 13!, respectively.
%C This sequence is complete by Saunders, Theorem 2.
%C More generally, Saunders, Theorem 2 states that, for any positive integers a, b, c, m with gcd(b, c) = 1, there are only finitely many solutions to phi(a*n!/b) = cx^m and these solutions satisfy n <= max {61, 3a, 3b, 3c}.
%H J. C. Saunders, <a href="https://arxiv.org/abs/1902.01638">Diophantine equations involving the Euler totient function</a>, arXiv:1902.01638 [math.NT], 2019-2020.
%H J. C. Saunders, <a href="https://doi.org/10.1016/j.jnt.2019.09.001">Diophantine equations involving the Euler totient function</a>, J. Number Theory 209 (2020), 347-358.
%e a(4) = 9216 = 96^2 and phi(8!) = phi(40320) = 9216.
%Y Cf. A000010 (totient), A000142 (factorial numbers), A001597 (perfect powers).
%K nonn,fini,full
%O 1,2
%A _Tomohiro Yamada_, Jul 17 2020