A195418 a(n) = phi(C(n)) / gcd(C(n)-1, phi(C(n))), where C(n) is the n-th Cullen number.

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

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. 129-134, 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 * A366857 A065974 A096822

Adjacent sequences: A195415 A195416 A195417 * A195419 A195420 A195421

Keyword

nonn,easy

Author

Alonso del Arte, Sep 20 2011

Status

approved