A326618 a(n) = n^18 + n^9 + 1.

1, 3, 262657, 387440173, 68719738881, 3814699218751, 101559966746113, 1628413638264057, 18014398643699713, 150094635684419611, 1000000001000000001, 5559917315850179173, 26623333286045024257, 112455406962561892503, 426878854231297789441, 1477891880073843750001

Offset

0,2

Comments

a(n) = Phi_27(n) where Phi_k(x) is the k-th cyclotomic polynomial.

Links

Richard N. Smith, Table of n, a(n) for n = 0..2000

OEIS Wiki, Cyclotomic Polynomials at x=n, n! and sigma(n)

Eric Weisstein's World of Mathematics, Cyclotomic Polynomial

Index to values of cyclotomic polynomials of integer argument

Mathematica

Table[n^18 + n^9 + 1, {n, 0, 17}] (* Vincenzo Librandi, Jul 15 2019 *)
Table[Cyclotomic[27, n], {n, 0, 17}]

Prog

(Magma) [n^18+n^9+1: n in [0..17]]; // Vincenzo Librandi, Jul 15 2019
(PARI) a(n) = polcyclo(27, n); \\ Michel Marcus, Jul 20 2019

Crossrefs

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).

Cf. A153440 (indices of prime terms).

Sequence in context: A176586 A339776 A033982 * A366680 A154824 A261541

Adjacent sequences: A326615 A326616 A326617 * A326619 A326620 A326621

Keyword

nonn

Author

Richard N. Smith, Jul 15 2019

Status

approved