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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, 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, 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 > 29. - T. D. Noe, Jun 21 2012

LINKS

T. D. Noe, 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.

Eric W. Weisstein, MathWorld: Fermat prime

Wikipedia, Euler's totient function

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)]; a(n)=A014197(2^n)=A014197(A000079(n))

CROSSREFS

Cf. A014197, A000079, A058213.

Sequence in context: A167975 A008684 A188462 * 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

STATUS

approved

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Last modified August 19 18:51 EDT 2019. Contains 326133 sequences. (Running on oeis4.)