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A336220
Perfect powers which are totients of factorials.
0
1, 8, 32, 9216, 82944, 8294400, 1194393600
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
Cf. A000010 (totient), A000142 (factorial numbers), A001597 (perfect powers).
Sequence in context: A288457 A166995 A079271 * A247533 A240547 A031445
KEYWORD
nonn,fini,full
AUTHOR
Tomohiro Yamada, Jul 17 2020
STATUS
approved