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

Author

Alonso del Arte, Sep 20 2011

Keywords

• nonn
• easy

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."

Examples

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

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.

Crossrefs

Cf. A000010, A002064, A005849, A160595.

Programs

Mathematica

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

PARI

a(n)=my(C=n<Charles R Greathouse IV, Feb 05 2013