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%I #26 Sep 08 2022 08:46:24
%S 1,3,262657,387440173,68719738881,3814699218751,101559966746113,
%T 1628413638264057,18014398643699713,150094635684419611,
%U 1000000001000000001,5559917315850179173,26623333286045024257,112455406962561892503,426878854231297789441,1477891880073843750001
%N a(n) = n^18 + n^9 + 1.
%C a(n) = Phi_27(n) where Phi_k(x) is the k-th cyclotomic polynomial.
%H Richard N. Smith, <a href="/A326618/b326618.txt">Table of n, a(n) for n = 0..2000</a>
%H OEIS Wiki, <a href="https://oeis.org/wiki/Cyclotomic Polynomials at x=n, n! and sigma(n)">Cyclotomic Polynomials at x=n, n! and sigma(n)</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CyclotomicPolynomial.html">Cyclotomic Polynomial</a>
%H <a href="/index/Cy#CyclotomicPolynomialsValuesAtX">Index to values of cyclotomic polynomials of integer argument</a>
%t Table[n^18 + n^9 + 1, {n, 0, 17}] (* _Vincenzo Librandi_, Jul 15 2019 *)
%t Table[Cyclotomic[27, n], {n, 0, 17}]
%o (Magma) [n^18+n^9+1: n in [0..17]]; // _Vincenzo Librandi_, Jul 15 2019
%o (PARI) a(n) = polcyclo(27, n); \\ _Michel Marcus_, Jul 20 2019
%Y Sequences of the type Phi_k(n), where Phi_k is the k-th cyclotomic polynomial: A000012 (k=0), A023443 (k=1), A000027 (k=2), A002061 (k=3), A002522 (k=4), A053699 (k=5), A002061 (k=6), A053716 (k=7), A002523 (k=8), A060883 (k=9), A060884 (k=10), A060885 (k=11), A060886 (k=12), A060887 (k=13), A060888 (k=14), A060889 (k=15), A060890 (k=16), A269442 (k=17), A060891 (k=18), A269446 (k=19), A060892 (k=20), A269483 (k=21), A269486 (k=22), A060893 (k=24), A269527 (k=25), A266229 (k=26), this sequence (k=27), A270204 (k=28), A060894 (k=30), A060895 (k=32), A060896 (k=36).
%Y Cf. A153440 (indices of prime terms).
%K nonn
%O 0,2
%A _Richard N. Smith_, Jul 15 2019
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