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A376482
a(n) = phi( 2^(2*n) + 2^n + 1 ) / (6*n), where phi() is Euler's totient function (A000010).
1
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
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
KEYWORD
nonn
AUTHOR
Max Alekseyev, Sep 24 2024
STATUS
approved