A066669 Numbers m such that phi(m) = 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

Author

Labos Elemer, Dec 18 2001

Keywords

• nonn

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

Products of powers of 2, distinct terms (at least one) of A074781, and possibly (if all the factors from A074781 are Fermat primes, A019434) an additional Fermat prime (i.e., it can be divisible by a square of one Fermat prime, A330828). - Amiram Eldar, Feb 11 2025

Examples

			7 is a term because phi(7) = 6 divided by 2 is 3, a prime.
21 is a term because phi(21) = 12 divided by 4 is 3, a prime.
15 is not a term because phi(15) = 8 divided by 8 is 1, not a prime.
		

Links

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

Crossrefs

Cf. A000010, A066670, A066671, A066672, A066673, A065966.

Cf. A019434, A058500, A074781, A330828.

Programs

Mathematica

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

PARI

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