A066669 Numbers n such that phi(n) = 2^k*prime for some k >= 0.

7, 9, 11, 13, 14, 18, 21, 22, 23, 25, 26, 28, 29, 33, 35, 36, 39, 41, 42, 44, 45, 46, 47, 50, 52, 53, 55, 56, 58, 59, 65, 66, 69, 70, 72, 75, 78, 82, 83, 84, 87, 88, 89, 90, 92, 94, 97, 100, 104, 105, 106, 107, 110, 112, 113, 115, 116, 118, 119, 123, 130, 132, 137, 138

Offset

1,1

Comments

Sequence is infinite, since 2n is in the sequence if and only if n is in the sequence. What is its density? - Charles R Greathouse IV, Feb 21 2013

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

7 is here because phi(7)=6 divided by 2 is prime; 21 is here because phi(21)=12 divided by 4 is prime; 15 is not here because phi(15)=8 divided by 8 is not prime.

Mathematica

Select[Range@ 138, PrimeQ@ Last@ Most@ NestWhileList[#/2 &, EulerPhi@ #, IntegerQ@ # &] &] (* Michael De Vlieger, Mar 18 2017 *)

Prog

(PARI) is(n)=n=eulerphi(n); isprime(n>>valuation(n, 2)) \\ Charles R Greathouse IV, Feb 21 2013

Crossrefs

Cf. A000010, A066670-A066673, A065966.

Sequence in context: A360796 A004169 A295299 * A059808 A020742 A193071

Adjacent sequences: A066666 A066667 A066668 * A066670 A066671 A066672

Keyword

nonn

Author

Labos Elemer, Dec 18 2001

Status

approved