A227533 Smallest e > 1 such that (2n)^e is a totient, or 0 if no such e exists.

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 4, 2, 3, 2, 2, 2, 4, 2, 2, 2, 2, 2, 3, 2, 5, 2, 2, 2, 2, 2, 2, 3, 3, 2, 4, 2, 15, 2, 2, 4, 2, 2, 3, 2, 3, 2, 4, 2, 2, 2, 2, 2, 3, 2, 7, 2, 2, 2, 2, 2, 2, 2, 4, 2, 3, 2, 2, 2, 2, 3, 3, 2, 8, 2, 2, 4, 15, 2, 2, 3, 2, 2, 5, 2, 4, 2, 2

Offset: 1

Author

Charles R Greathouse IV, Jul 14 2013

Keywords

• nonn

Comments

Conjecture: a(n) > 0 for all n.

Examples

			a(1) = 2 because phi(5) = 2^2. a(11) = 3 because phi(13315) = 22^3 but phi(k) is not equal to 22^2 for any k.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..100000
• Charles R Greathouse IV, GP script for efficiently computing the sequence

Crossrefs

Cf. A000010, A002202, A065528, A227534, A227535.

Programs

PARI

a(n)=my(k=2);while(!istotient((2*n)^k),k++);k