

A195418


a(n) = phi(C(n)) / gcd(C(n)1, phi(C(n)), where C(n) is the nth Cullen number.


1



1, 1, 3, 5, 3, 33, 5, 33, 341, 1045, 189, 1299, 891, 4437, 9477, 581, 3855, 105525, 27825, 23751, 173043, 10531345, 56511, 2386125, 380955, 256861, 24926139, 5108467, 32397379, 930343095, 930291, 36512775
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OFFSET

0,3


COMMENTS

When C(n) is prime (or 1), then a(n) = 1; that is, n is in A005849.
On the penultimate page of their paper, Grau and Luca ask for "a good (large) lower bound on this quantity which is valid for all n and which tends to infinity with n."


LINKS

Amiram Eldar, Table of n, a(n) for n = 0..848
José María Grau Ribas and Florian Luca, Cullen numbers with the Lehmer property, Proceedings of the American Mathematical Society, Vol. 140, No. 1 (2012), pp. 129134, preprint, arXiv:1103.3578 [math.NT], Mar 18, 2011.


EXAMPLE

a(2) = 3 because the second Cullen number is 9; phi(9) = 6, therefore 6/gcd(8, 6) = 6/2 = 3.


MATHEMATICA

cullen[n_] := n(2^n) + 1; Table[EulerPhi[cullen[n]]/GCD[cullen[n]  1, EulerPhi[cullen[n]]], {n, 0, 39}]


PROG

(PARI) a(n)=my(C=n<<n, p=eulerphi(C+1)); p/gcd(C, p) \\ Charles R Greathouse IV, Feb 05 2013


CROSSREFS

Cf. A000010, A002064, A005849, A160595.
Sequence in context: A080349 A249012 A249908 * A065974 A096822 A195383
Adjacent sequences: A195415 A195416 A195417 * A195419 A195420 A195421


KEYWORD

nonn,easy


AUTHOR

Alonso del Arte, Sep 20 2011


STATUS

approved



