A066792 a(n) = phi(n^3 + n^2 + n + 1).

1, 2, 8, 16, 64, 48, 216, 160, 288, 320, 1000, 480, 1344, 768, 1568, 1792, 4096, 1344, 4320, 2880, 4800, 3840, 8448, 3328, 11520, 7488, 12168, 6912, 17472, 6720, 24960, 13824, 16000, 13824, 25344, 14688, 46656, 19584, 26112, 24320, 64000, 19488

Offset: 0

Author

Benoit Cloitre, Jan 18 2002

Keywords

• nonn
• easy

Links

• Harry J. Smith, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000010 (phi), A053698, A243379.

Programs

Mathematica

Prepend[EulerPhi[Total[#^Range[0,3]]]&/@Range[45],1]  (* Harvey P. Dale, Feb 19 2011 *)

PARI

a(n) = eulerphi(n^3 + n^2 + n + 1); \\ Harry J. Smith, Mar 27 2010

Formula

a(n) = A000010(A053698(n)). - Michel Marcus, Sep 06 2022

Sum_{k=1..n} a(k) = c * n^4 + O((n*log(n))^3), where c = (3/16) * Product_{primes p == 1 (mod 4)} (1 - 3/p^2) * Product_{primes p == 3 (mod 4)} (1 - 1/p^2) = 0.13549316168... . - Amiram Eldar, Dec 09 2024