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A032446
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Number of solutions to phi(k) = 2n.
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8
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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; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(n) = Number of Galois Fields GF(k) with 2n elements. - Artur Jasinski, Oct 13 2011
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REFERENCES
| Albert H. Beiler, "Recreations in the Theory of Numbers, The Queen of Mathematics Entertains, " Second Edition, Dover Publications, Inc., NY, 1966, page 90.
Carl Pomerance, Popular values of Euler's function.Mathematica 27 (1980), 84-89.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..5000
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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
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MAPLE
| with(numtheory); [ seq(nops(invphi(2*n)), n=1..90) ];
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MATHEMATICA
| t = Table[0, {100} ]; Do[a = EulerPhi[n]; If[a < 202, t[[a/2]]++ ], {n, 3, 10^5} ]; t
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CROSSREFS
| Bisection of A014197.
Cf. A000010 and A005277.
Cf. A085758.
Sequence in context: A112180 A185271 A158012 * A028949 A107574 A053405
Adjacent sequences: A032443 A032444 A032445 * A032447 A032448 A032449
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KEYWORD
| nonn,easy,nice
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AUTHOR
| Ursula Gagelmann (gagelmann(AT)altavista.net)
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EXTENSIONS
| Extended by Robin Trew (trew(AT)hcs.harvard.edu).
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