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A239363 Numbers k such that phi(k+1) - phi(k) = k/2.

%I A239363 #18 Nov 09 2024 04:21:44
%S A239363 2,4,16,24,216,256,4960,10648,65536,195112,1191016,7544800,11530464,
%T A239363 12705504,45882712,55742968,179883264,946966168,2106997768,2289529432,
%U A239363 2548895896,3056745600,3482123272,7756683264,10735357816,15920801280,26946035992,46827274240
%N A239363 Numbers k such that phi(k+1) - phi(k) = k/2.
%C A239363 From _Amiram Eldar_, Nov 09 2024: (Start)
%C A239363 If p is a Fermat prime (A019434), then p-1 is a term.
%C A239363 If p is a term of A237038, then 8*p^3 is a term. (End)
%H A239363 Giovanni Resta, <a href="/A239363/b239363.txt">Table of n, a(n) for n = 1..39</a> (terms < 10^12)
%e A239363 phi(217) = 180, phi(216) = 72, and 180-72 = 108, which is 216/2.
%p A239363 with(numtheory); P:=proc(q) local n;
%p A239363 for n from 1 to q do if phi(n+1)-phi(n)=n/2 then print(n);
%p A239363 fi; od; end: P(10^9);
%t A239363 Select[Range[200000], EulerPhi[#+1] - EulerPhi[#] == #/2 &] (* _Amiram Eldar_, Nov 09 2024 *)
%o A239363 (PARI) is(k) = eulerphi(k+1) - eulerphi(k) == k/2; \\ _Amiram Eldar_, Nov 09 2024
%Y A239363 Cf. A000010, A019434, A237038.
%K A239363 nonn
%O A239363 1,1
%A A239363 _Paolo P. Lava_, Mar 17 2014
%E A239363 a(13)-a(27) from _Giovanni Resta_, Mar 17 2014