The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A335723 Perfect powers whose totients are factorials. 0
 1, 4, 9, 225, 11025, 176400, 1587600, 192099600, 32464832400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Corresponding values of factorials are 1!, 2!, 3!, 5!, 7!, 8!, 9!, 11! and 13!, respectively. This sequence is complete by Saunders, Theorem 1. All integers in this sequence are square. Hence, there exists no m-th power with m >= 3 whose totient is a factorial except 1. More generally, Saunders, Theorem 1 states that, for any positive integers a, b, c, m with gcd(b, c) = 1, there are only finitely many solutions to phi(ax^m) = b*n!/c 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(5) = 11025 = 105^2 and phi(11025) = 5040 = 7!. CROSSREFS Cf. A000010 (totient), A000142 (factorial numbers), A001597 (perfect powers). Sequence in context: A286322 A318615 A030074 * A299122 A167657 A175700 Adjacent sequences:  A335720 A335721 A335722 * A335724 A335725 A335726 KEYWORD nonn,fini,full AUTHOR Tomohiro Yamada, Jun 19 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 27 20:49 EST 2021. Contains 349395 sequences. (Running on oeis4.)