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A032446 Number of solutions to phi(k) = 2n. 11
3, 4, 4, 5, 2, 6, 0, 6, 4, 5, 2, 10, 0, 2, 2, 7, 0, 8, 0, 9, 4, 3, 2, 11, 0, 2, 2, 3, 2, 9, 0, 8, 2, 0, 2, 17, 0, 0, 2, 10, 2, 6, 0, 6, 0, 3, 0, 17, 0, 4, 2, 3, 2, 9, 2, 6, 0, 3, 0, 17, 0, 0, 2, 9, 2, 7, 0, 2, 2, 3, 0, 21, 0, 2, 2, 0, 0, 7, 0, 12, 4, 3, 2, 12, 0, 2, 0, 8, 2, 10 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) is the number of Galois Fields GF(k) with 2n elements. - Artur Jasinski, Oct 13 2011

By Carmichael's conjecture, a(n) <> 1 for any n. See A074987. - Thomas Ordowski, Sep 13 2017

REFERENCES

Albert H. Beiler, "Recreations in the Theory of Numbers, The Queen of Mathematics Entertains," Second Edition, Dover Publications, Inc., NY, 1966, page 90.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..5000

Matteo Caorsi, Sergio Cecotti, Geometric classification of 4d N=2 SCFTs, arXiv:1801.04542 [hep-th], 2018.

Carl Pomerance, Popular values of Euler's function, Mathematica 27 (1980), 84-89.

EXAMPLE

If n=8 then phi(x)=2*8=16 is satisfied for only a(8)=6 values of x, viz. 17, 32, 34, 40, 48, 60.

For 2n=16 we have 6 different of Galois Fields GF(k) with 16 elements : GF(17), GF(32), GF(34), GF(40), GF(48), GF(60). - Artur Jasinski, Oct 13 2011

MAPLE

with(numtheory); [ seq(nops(invphi(2*n)), n=1..90) ];

MATHEMATICA

t = Table[0, {100} ]; Do[a = EulerPhi[n]; If[a < 202, t[[a/2]]++ ], {n, 3, 10^5} ]; t

CROSSREFS

Bisection of A014197.

Cf. A000010, A005277, A085758.

Sequence in context: A232092 A185271 A158012 * A271563 A028949 A201006

Adjacent sequences:  A032443 A032444 A032445 * A032447 A032448 A032449

KEYWORD

nonn,easy,nice

AUTHOR

Ursula Gagelmann (gagelmann(AT)altavista.net)

EXTENSIONS

Extended by Robin Trew (trew(AT)hcs.harvard.edu).

STATUS

approved

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Last modified August 16 16:40 EDT 2018. Contains 313809 sequences. (Running on oeis4.)