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A258454 Numbers n such that phi(n) = 2*phi(n-2). 0

%I #26 Sep 08 2022 08:46:12

%S 3,4,5,8,17,32,257,512,527,992,1952,2522,5252,6512,7412,10376,23432,

%T 23717,26732,27302,35114,36632,37442,45872,47027,49022,51092,65537,

%U 78899,84242,92432,98432,98672,114767,115292,131072,227222,231167,240977,328352,369272

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

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

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

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

%t Select[Range@ 400000, EulerPhi@ # == 2 EulerPhi[# - 2] &] (* _Michael De Vlieger_, Sep 25 2015 *)

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

%o (PARI) for(n=1, 1e6, if(eulerphi(n) == 2*eulerphi(n-2), print1(n", "))); \\ _Altug Alkan_, Sep 26 2015

%Y Cf. A171271, A171262.

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Sep 24 2015

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Last modified March 28 12:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)