A319213 a(n) = phi(n^3 - 1)/3 where phi is A000010.

2, 4, 12, 20, 56, 36, 144, 96, 216, 144, 520, 240, 840, 480, 576, 816, 1568, 756, 2520, 1232, 1872, 1560, 4400, 1440, 4320, 3024, 4860, 3168, 7056, 2640, 9000, 5984, 7920, 6144, 10080, 4752, 17784, 7992, 13104, 9184, 22080, 7560, 23688, 12960, 14688, 15840, 33120

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 3 of A369291.

Cf. A000010, A068601 (n^3-1).

phi(n^b - 1)/b: A319210 (b=2), this sequence (b=3), A319214 (b=5).

Programs

Mathematica

EulerPhi[Range[2, 50]^3 - 1]/3 (* Paolo Xausa, Jun 18 2024 *)

PARI

{a(n) = eulerphi(n^3-1)/3}

Formula

Sum_{k=1..n} a(k) = c * n^4 + O((n*log(n))^3), where c = (2/27) * Product_{p prime == 1 (mod 3)} (1 - 3/p^2) * Product_{p prime == 2 (mod 3)} (1 - 1/p^2) = 0.047313356295... . - Amiram Eldar, Dec 09 2024