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%I #8 Oct 18 2024 18:13:44
%S 3,7,9,31,127,8191,131071,524287
%N Numbers k such that phi(k)/2 + 1 = phi(k + 1) where phi = A000010.
%C Conjecture: this sequence is the union {9} and the Mersenne primes A000668.
%e Number 9 is in this sequence because phi(9)/2 + 1 = 6/2 + 1 = 3 + 1 = 4 is equal to phi(9 + 1) = phi(10) = 4.
%t Select[Range[550000], EulerPhi[#]/2+1==EulerPhi[#+1] &] (* _Stefano Spezia_, Sep 22 2024 *)
%o (Magma) [k: k in [3..5*10^6] | ((EulerPhi(k) div 2) + 1) eq EulerPhi(k + 1)];
%Y Cf. A000010, A000668, A191611, A376338.
%K nonn,more
%O 1,1
%A _Juri-Stepan Gerasimov_, Sep 20 2024