

A143510


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


1




OFFSET

1,1


COMMENTS

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.


REFERENCES

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


LINKS

Table of n, a(n) for n=1..9.
T. D. Noe, Numbers Like 16842752
William P. Wardlaw, L. L. Foster and R. J. Simpson, Problem E3361, Amer. Math. Monthly, Vol. 98, No. 5 (May, 1991), 443444.
E. W. Weisstein, MathWorld: Carmichaels Totient Function Conjecture


CROSSREFS

Cf. A143511 (least k such that phi(k)=n).
Sequence in context: A230636 A283029 A250933 * A043680 A204673 A205640
Adjacent sequences: A143507 A143508 A143509 * A143511 A143512 A143513


KEYWORD

more,nonn


AUTHOR

T. D. Noe, Aug 21 2008


STATUS

approved



