This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A250222 #19 Aug 02 2025 17:26:25
%S A250222 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 A250222 12,30,44,6,16,46,12,46,48,4,24,54,22,42,40,14,48,48,16,26,64,18,60,
%U A250222 70,0,54,72,32,64,52,16,38,78,20,40,90,20,82,68,6,72,94,44,50,64
%N A250222 a(n) = phi(2n+1) - phi(2n), where phi is A000010.
%C A250222 a(157) = -12 is the first negative number in this sequence.
%H A250222 Amiram Eldar, <a href="/A250222/b250222.txt">Table of n, a(n) for n = 1..10000</a>
%F A250222 From _Amiram Eldar_, Nov 09 2024: (Start)
%F A250222 a(n) = A057000(2*n).
%F A250222 a(n) = A037225(n) - A062570(n).
%F A250222 Sum_{k=1..n} a(k) ~ c * n^2, where c = 4/Pi^2 = 0.405284... (A185199). (End)
%t A250222 a[n_] := EulerPhi[2*n+1] - EulerPhi[2*n]; Array[a, 100] (* _Amiram Eldar_, Nov 09 2024 *)
%t A250222 #[[2]]-#[[1]]&/@Partition[EulerPhi[Range[2,150]],2] (* _Harvey P. Dale_, Aug 02 2025 *)
%o A250222 (PARI) a(n) = eulerphi(2*n+1) - eulerphi(2*n); \\ _Amiram Eldar_, Nov 09 2024
%Y A250222 Cf. A000010, A037225, A057000, A062570, A185199.
%K A250222 nonn,easy
%O A250222 1,2
%A A250222 _Eric Chen_, Dec 24 2014