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 A336220 Perfect powers which are totients of factorials. 0
 1, 8, 32, 9216, 82944, 8294400, 1194393600 (list; graph; refs; listen; history; text; internal format)
 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 Adjacent sequences:  A336217 A336218 A336219 * A336221 A336222 A336223 KEYWORD nonn,fini,full AUTHOR Tomohiro Yamada, Jul 17 2020 STATUS approved

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Last modified September 27 18:56 EDT 2021. Contains 347694 sequences. (Running on oeis4.)