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A143510 Numbers n such that the equation phi(x) = n has no odd solutions. 1


%S 16842752,33685504,67371008,134742016,269484032,538968064,1077936128,

%T 2155872256,4294967296

%N Numbers n such that the equation phi(x) = n has no odd solutions.

%C In the unlikely event that Carmichael's conjecture is proved false, the counterexamples will be in this sequence. The number a(1) = 16842752 = 257*2^16 is mentioned in problem E3361. If there are only five Fermat primes, then 2^k is in this sequence for all k>31. It appears that for every product d of Fermat primes (A143512), the number 2^k * d is in this sequence for some k. The link to "Numbers Like 16842752" lists examples for various d.

%D R. K. Guy, Unsolved problems in number theory, B39.

%H T. D. Noe, <a href="http://www.sspectra.com/math/16842752.txt">Numbers Like 16842752</a>

%H William P. Wardlaw, L. L. Foster and R. J. Simpson, <a href="http://www.jstor.org/stable/2323869">Problem E3361</a>, Amer. Math. Monthly, Vol. 98, No. 5 (May, 1991), 443-444.

%H E. W. Weisstein, <a href="http://mathworld.wolfram.com/CarmichaelsTotientFunctionConjecture.html">MathWorld: Carmichaels Totient Function Conjecture</a>

%Y Cf. A143511 (least k such that phi(k)=n).

%K more,nonn

%O 1,1

%A _T. D. Noe_, Aug 21 2008

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