A269442 a(n) = n*(n^8 + 1)*(n^4 + 1)*(n^2 + 1)*(n + 1) + 1.

1, 17, 131071, 64570081, 5726623061, 190734863281, 3385331888947, 38771752331201, 321685687669321, 2084647712458321, 11111111111111111, 50544702849929377, 201691918794585181, 720867993281778161, 2345488209948553531, 7037580381120954241

Offset: 0

Author

Ilya Gutkovskiy, Feb 26 2016

Keywords

• nonn
• easy

Comments

a(n) = Phi_17(n) where Phi_k(x) is the k-th cyclotomic polynomial.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• 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
• Index entries for linear recurrences with constant coefficients, signature (17, -136, 680, -2380, 6188, -12376, 19448, -24310, 24310, -19448, 12376, -6188, 2380, -680, 136, -17, 1).

Crossrefs

Cf. similar sequences of the type Phi_k(n), where Phi_k is the k-th cyclotomic polynomial: A000012 (k=0), A023443 (k=1), A000027 (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), this sequence (k=17), A060891 (k=18), A269446 (k=19).

Programs

GAP

List([0..20], n-> n*(n^8+1)*(n^4+1)*(n^2+1)*(n+1)+1); # G. C. Greubel, Apr 24 2019

Magma

[n*(n^8+1)*(n^4+1)*(n^2+1)*(n+1)+1: n in [0..20]]; // Vincenzo Librandi, Feb 27 2016

Mathematica

Table[Cyclotomic[17, n], {n, 0, 15}]

PARI

a(n)=n*(n^8+1)*(n^4+1)*(n^2+1)*(n+1)+1 \\ Charles R Greathouse IV, Jul 26 2016

Sage

[n*(n^8+1)*(n^4+1)*(n^2+1)*(n+1)+1 for n in (0..20)] # G. C. Greubel, Apr 24 2019

Formula

G.f.: (1 +130918*x^2 [phone]*x^3 [phone]*x^4 [phone]*x^5 [phone]*x^6 [phone]*x^7 [phone]*x^8 [phone]*x^9 [phone]*x^10 [phone]*x^11 [phone]*x^12 [phone]*x^13 [phone]*x^14 +43674*x^15 +x^16)/(1 - x)^17.

Sum_{n>=0} 1/a(n) = 1.05883117453...