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

2,1

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^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

Mathematica

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

Prog

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

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).

Sequence in context: A297184 A218871 A121569 * A099603 A319615 A375742

Adjacent sequences: A319210 A319211 A319212 * A319214 A319215 A319216

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 13 2018

Status

approved