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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.

%I A269446 #23 Feb 16 2025 08:33:30
%S A269446 1,19,524287,581130733,91625968981,4768371582031,121871948002099,
%T A269446 1899815864228857,20587884010836553,168856464709124011,
%U A269446 1111111111111111111,6115909044841454629,29043636306420266077,121826690864620509223,459715689149916492091,1583455585752214704241
%N 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.
%C A269446 a(n) = Phi_19(n) where Phi_k(x) is the k-th cyclotomic polynomial.
%H A269446 G. C. Greubel, <a href="/A269446/b269446.txt">Table of n, a(n) for n = 0..1000</a>
%H A269446 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 A269446 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CyclotomicPolynomial.html">Cyclotomic Polynomial</a>
%H A269446 <a href="/index/Cy#CyclotomicPolynomialsValuesAtX">Index to values of cyclotomic polynomials of integer argument</a>
%H A269446 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (19, -171, 969, -3876, 11628, -27132, 50388, -75582, 92378, -92378, 75582, -50388, 27132, -11628, 3876, -969, 171, -19, 1).
%F A269446 Sum_{n>=0} 1/a(n) = 1.0526334880315548541801483535546024...
%t A269446 Table[Cyclotomic[19, n], {n, 0, 15}]
%o A269446 (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
%o A269446 (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
%o A269446 (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
%o A269446 (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
%Y A269446 Cf. similar sequences of the type Phi_k(n) listed in A269442.
%K A269446 nonn,easy
%O A269446 0,2
%A A269446 _Ilya Gutkovskiy_, Feb 27 2016