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

1,2

Comments

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

Links

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

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)

Mathematica

a[n_] := EulerPhi[2*n+1] - EulerPhi[2*n]; Array[a, 100] (* Amiram Eldar, Nov 09 2024 *)

Prog

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

Crossrefs

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

Sequence in context: A083791 A303347 A325971 * A026251 A205721 A378220

Adjacent sequences: A250219 A250220 A250221 * A250223 A250224 A250225

Keyword

nonn,easy

Author

Eric Chen, Dec 24 2014

Status

approved