A250222 - OEIS

%I #17 Nov 09 2024 04:19:56

%S 1,2,4,2,6,8,2,8,12,4,12,12,6,16,22,4,8,24,6,24,30,4,24,26,12,28,22,

%T 12,30,44,6,16,46,12,46,48,4,24,54,22,42,40,14,48,48,16,26,64,18,60,

%U 70,0,54,72,32,64,52,16,38,78,20,40,90,20,82,68,6,72,94,44,50,64

%N a(n) = phi(2n+1) - phi(2n), where phi is A000010.

%C a(157) = -12 is the first negative number in this sequence.

%H Amiram Eldar, <a href="/A250222/b250222.txt">Table of n, a(n) for n = 1..10000</a>

%F From _Amiram Eldar_, Nov 09 2024: (Start)

%F a(n) = A057000(2*n).

%F a(n) = A037225(n) - A062570(n).

%F Sum_{k=1..n} a(k) ~ c * n^2, where c = 4/Pi^2 = 0.405284... (A185199). (End)

%t a[n_] := EulerPhi[2*n+1] - EulerPhi[2*n]; Array[a, 100] (* _Amiram Eldar_, Nov 09 2024 *)

%o (PARI) a(n) = eulerphi(2*n+1) - eulerphi(2*n); \\ _Amiram Eldar_, Nov 09 2024

%Y Cf. A000010, A037225, A057000, A062570, A185199.

%K nonn,easy

%O 1,2

%A _Eric Chen_, Dec 24 2014