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Search: id:A143510
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| A143510 |
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Numbers n such that the equation phi(x) = n has no odd solutions. |
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+0
2
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| 16842752, 33685504, 67371008, 134742016, 269484032, 538968064, 1077936128, 2155872256, 4294967296
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
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REFERENCES
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R. K. Guy, Unsolved problems in number theory, B39.
William P. Wardlaw, L. L. Foster and R. J. Simpson, Problem E3361, Amer. Math. Monthly, Vol. 98, No. 5 (May, 1991), 443-444.
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LINKS
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T. D. Noe, Numbers Like 16842752
E. W. Weisstein, MathWorld: Carmichaels Totient Function Conjecture
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CROSSREFS
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Cf. A143511 (least k such that phi(k)=n).
Sequence in context: A017711 A013972 A036102 this_sequence A043680 A129478 A032749
Adjacent sequences: A143507 A143508 A143509 this_sequence A143511 A143512 A143513
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KEYWORD
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more,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Aug 21 2008
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