# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a336220
Showing 1-1 of 1

%I A336220 #11 Aug 07 2020 17:34:47
%S A336220 1,8,32,9216,82944,8294400,1194393600
%N A336220 Perfect powers which are totients of factorials.
%C A336220 Corresponding values of factorials are 1! (and 2!), 4!, 5!, 8!, 9!, 11! and 13!, respectively.
%C A336220 This sequence is complete by Saunders, Theorem 2.
%C A336220 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 A336220 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 A336220 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 A336220 a(4) = 9216 = 96^2 and phi(8!) = phi(40320) = 9216.
%Y A336220 Cf. A000010 (totient), A000142 (factorial numbers), A001597 (perfect powers).
%K A336220 nonn,fini,full
%O A336220 1,2
%A A336220 _Tomohiro Yamada_, Jul 17 2020

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE