A258454 Numbers n such that phi(n) = 2*phi(n-2).

3, 4, 5, 8, 17, 32, 257, 512, 527, 992, 1952, 2522, 5252, 6512, 7412, 10376, 23432, 23717, 26732, 27302, 35114, 36632, 37442, 45872, 47027, 49022, 51092, 65537, 78899, 84242, 92432, 98432, 98672, 114767, 115292, 131072, 227222, 231167, 240977, 328352, 369272

Offset: 1

Author

Jaroslav Krizek, Sep 24 2015

Keywords

• nonn

Comments

Conjecture: a prime p is in the sequence iff p is a Fermat prime (A019434).

This is not correct: the first non-Fermat prime term is 83623937 = 2^18*11*29 + 1. - Joerg Arndt, Oct 11 2015

Examples

			phi(32) = 16 = 2*phi(30) = 2*8, so 32 is in the sequence.
		

Crossrefs

Cf. A171271, A171262.

Programs

Magma

[n: n in [3..10000000] | EulerPhi(n) eq 2*EulerPhi(n-2)];

Mathematica

Select[Range@ 400000, EulerPhi@ # == 2 EulerPhi[# - 2] &] (* Michael De Vlieger, Sep 25 2015 *)

PARI

for(n=1, 1e6, if(eulerphi(n) == 2*eulerphi(n-2), print1(n", "))); \\ Altug Alkan, Sep 26 2015