A319210 a(n) = phi(n^2 - 1)/2 where phi is A000010.

1, 2, 4, 4, 12, 8, 18, 16, 30, 16, 60, 24, 48, 48, 64, 48, 144, 48, 108, 80, 132, 80, 220, 96, 180, 144, 252, 96, 420, 128, 300, 256, 240, 192, 432, 216, 432, 288, 480, 192, 840, 240, 504, 440, 552, 352, 966, 320, 672, 480, 832, 432, 1040, 432, 720, 672, 1044, 448

Offset

2,2

Links

Seiichi Manyama, Table of n, a(n) for n = 2..1000

Eric Weisstein's World of Mathematics, Totient Function.

Wikipedia, Euler's totient function.

Formula

Sum_{k=1..n} a(k) = c * n^3 / 4 + O((n*log(n))^2), where c = Product_{p prime} (1 - 2/p^2) = 0.322634... (A065474). - Amiram Eldar, Dec 09 2024

Mathematica

Table[(EulerPhi@(n^2 - 1) / 2), {n, 2, 70}] (* Vincenzo Librandi, Sep 15 2018 *)

Prog

(PARI) {a(n) = eulerphi(n^2-1)/2}
(Magma) [EulerPhi(n^2-1)/2: n in [2..70]]; // Vincenzo Librandi, Sep 15 2018

Crossrefs

Row 2 of A369291.

Cf. A000010, A005563 (n^2-1, shifted), A065474.

phi(n^b - 1)/b: this sequence (b=2), A319213 (b=3), A319214 (b=5).

Sequence in context: A186973 A225232 A326824 * A292303 A000936 A376091

Adjacent sequences: A319207 A319208 A319209 * A319211 A319212 A319213

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 13 2018

Status

approved