A376482 a(n) = phi( 2^(2*n) + 2^n + 1 ) / (6*n), where phi() is Euler's totient function (A000010).

1, 1, 4, 6, 30, 72, 336, 720, 4864, 9900, 54498, 139968, 728208, 1820448, 11748240, 23224320, 142888536, 424189440, 2066689584, 4704480000, 34426570752, 75016279008, 437072997306, 1171108896768, 6391042560000, 16287748233120, 111155542830144, 225354102607872, 1419514150386528, 3983428743840000, 21252009311404938, 49614674429214720

Offset

1,3

Comments

In fact, phi(m^(2*n) + m^n + 1) is a multiple of 6*n for all m > 1 and n >= 1. This sequence gives the corresponding quotients for m = 2.

Links

Table of n, a(n) for n=1..32.

M. Alekseyev et al., Divisibility of φ(n^(2k) + n^k + 1) by 6k (in Russian), dxdy.ru, 2022.

Mathematica

a[n_]:= EulerPhi[2^(2*n) + 2^n + 1 ]/(6*n); Array[a, 32] (* Stefano Spezia, Sep 25 2024 *)

Crossrefs

Cf. A000010, A001576, A066791.

Sequence in context: A046849 A090530 A154667 * A093121 A248048 A209298

Adjacent sequences: A376479 A376480 A376481 * A376483 A376484 A376485

Keyword

nonn

Author

Max Alekseyev, Sep 24 2024

Status

approved