A250222 a(n) = phi(2n+1) - phi(2n), where phi is A000010.

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, 12, 30, 44, 6, 16, 46, 12, 46, 48, 4, 24, 54, 22, 42, 40, 14, 48, 48, 16, 26, 64, 18, 60, 70, 0, 54, 72, 32, 64, 52, 16, 38, 78, 20, 40, 90, 20, 82, 68, 6, 72, 94, 44, 50, 64

Offset: 1

Author

Eric Chen, Dec 24 2014

Keywords

• nonn
• easy

Comments

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Mathematica

a[n_] := EulerPhi[2*n+1] - EulerPhi[2*n]; Array[a, 100] (* Amiram Eldar, Nov 09 2024 *)
#[[2]]-#[[1]]&/@Partition[EulerPhi[Range[2,150]],2] (* Harvey P. Dale, Aug 02 2025 *)

PARI

a(n) = eulerphi(2*n+1) - eulerphi(2*n); \\ Amiram Eldar, Nov 09 2024

Formula

From Amiram Eldar, Nov 09 2024: (Start)

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

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

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