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

Author

Seiichi Manyama, Sep 13 2018

Keywords

• nonn
• easy

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.

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).

Programs

Magma

[EulerPhi(n^2-1)/2: n in [2..70]]; // Vincenzo Librandi, Sep 15 2018

Mathematica

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

PARI

{a(n) = eulerphi(n^2-1)/2}

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