A269446 a(n) = n*(n^6 + n^3 + 1)*(n^6 - n^3 + 1)*(n^2 + n + 1)*(n^2 - n + 1)*(n + 1) + 1.

1, 19, 524287, 581130733, 91625968981, 4768371582031, 121871948002099, 1899815864228857, 20587884010836553, 168856464709124011, 1111111111111111111, 6115909044841454629, 29043636306420266077, 121826690864620509223, 459715689149916492091, 1583455585752214704241

Offset: 0

Author

Ilya Gutkovskiy, Feb 27 2016

Keywords

• nonn
• easy

Comments

a(n) = Phi_19(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 (19, -171, 969, -3876, 11628, -27132, 50388, -75582, 92378, -92378, 75582, -50388, 27132, -11628, 3876, -969, 171, -19, 1).

Crossrefs

Cf. similar sequences of the type Phi_k(n) listed in A269442.

Programs

GAP

List([0..20], n-> n*(n^6+n^3+1)*(n^6-n^3+1)*(n^2+n+1)*(n^2-n+1)*(n+1)+1); # G. C. Greubel, Apr 24 2019

Magma

[n*(n^6+n^3+1)*(n^6-n^3+1)*(n^2+n+1)*(n^2-n+1)*(n+1)+1: n in [0..20]]; // G. C. Greubel, Apr 24 2019

Mathematica

Table[Cyclotomic[19, n], {n, 0, 15}]

PARI

a(n)=n*(n^6+n^3+1)*(n^6-n^3+1)*(n^2+n+1)*(n^2-n+1)*(n+1)+1 \\ Charles R Greathouse IV, Jul 26 2016

Sage

[n*(n^6+n^3+1)*(n^6-n^3+1)*(n^2+n+1)*(n^2-n+1)*(n+1)+1 for n in (0..20)] # G. C. Greubel, Apr 24 2019

Formula

Sum_{n>=0} 1/a(n) = 1.0526334880315548541801483535546024...