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 A058321 Number of x such that phi(x) = 2^n. 2
 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS If there are only 5 Fermat primes (A019434), then a(n) = 32 for n > 31. - T. D. Noe, Jun 21 2012 [Corrected by Jeppe Stig Nielsen, Oct 02 2021.] The first unknown term is a(8589934592) which depends on whether A000215(33) is composite or prime. - Jeppe Stig Nielsen, Oct 02 2021 LINKS Jeppe Stig Nielsen, Table of n, a(n) for n = 0..1000 R. D. Carmichael, On Euler's phi-function, Bull. Amer. Math. Soc. 13 (1907), 241-243. R. D. Carmichael, Erratum: On Euler's phi-function, Bull. Amer. Math. Soc. 54 (1948), 1192. R. D. Carmichael, Erratum: Erratum: On Euler's phi-function, Bull. Amer. Math. Soc. 55 (1949), 212. Mathematics Stack Exchange, Empirical Observation on number of solutions to phi(n) = m. Eric W. Weisstein, MathWorld: Fermat prime Wikipedia, Euler's totient function FORMULA a(n) = A014197(2^n) = A014197(A000079(n)). EXAMPLE For n = 0, a(0) = 2 because phi(1) = phi(2) = 1. For n = 5, invphi(32) gives 7 values as follows: Phi[{51,64,68,80,96,102,120}] = {32,32,32,32,32,32,32}. MAPLE with(numtheory):[seq(nops(invphi(2^i)), i=1..100)]; CROSSREFS Cf. A014197, A000079, A058213, A000010, A003401, A004729, A019434, A045544. Sequence in context: A008684 A188462 A352530 * A318892 A323404 A056064 Adjacent sequences: A058318 A058319 A058320 * A058322 A058323 A058324 KEYWORD nonn AUTHOR Labos Elemer, Dec 11 2000 EXTENSIONS Added a(0) and corrected a(31) - T. D. Noe, Jun 21 2012 Correction of a(31) reverted; true value is a(31) = 33. - Jeppe Stig Nielsen, Oct 02 2021 STATUS approved

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Last modified February 21 20:02 EST 2024. Contains 370237 sequences. (Running on oeis4.)