OFFSET
1,2
COMMENTS
Corresponding values of factorials are 1! (and 2!), 4!, 5!, 8!, 9!, 11! and 13!, respectively.
This sequence is complete by Saunders, Theorem 2.
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}.
LINKS
J. C. Saunders, Diophantine equations involving the Euler totient function, arXiv:1902.01638 [math.NT], 2019-2020.
J. C. Saunders, Diophantine equations involving the Euler totient function, J. Number Theory 209 (2020), 347-358.
EXAMPLE
a(4) = 9216 = 96^2 and phi(8!) = phi(40320) = 9216.
CROSSREFS
KEYWORD
nonn,fini,full
AUTHOR
Tomohiro Yamada, Jul 17 2020
STATUS
approved