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 A230586 a(n) = n^5 - 5*n^3 + 5*n. 2

%I

%S 1,2,123,724,2525,6726,15127,30248,55449,95050,154451,240252,360373,

%T 524174,742575,1028176,1395377,1860498,2441899,3160100,4037901,

%U 5100502,6375623,7893624,9687625,11793626,14250627,17100748,20389349,24165150,28480351,33390752

%N a(n) = n^5 - 5*n^3 + 5*n.

%C Numbers n such that the polynomial x^10 - n*x^5 + 1 is reducible (see paper in A231123).

%C Second row of A231123.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6, -15, 20, -15, 6, -1).

%F G.f.: x*(1 - 4*x + 126*x^2 - 4*x^3 + x^4)/(1 - x)^6. - _Vincenzo Librandi_, Jan 11 2015

%t Table[n^5-5n^3+5n,{n,30}] (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{1,2,123,724,2525,6726},30] (* _Harvey P. Dale_, Jan 10 2015 *)

%t CoefficientList[Series[(1 - 4 x + 126 x^2 - 4 x^3 + x^4) / (1 - x)^6, {x, 0, 40}], x] (* _Vincenzo Librandi_, Jan 11 2015 *)

%o (PARI) for(n=1,10^10,if(!polisirreducible(x^10-n*x^5+1),print1(n,", ")));

%o (MAGMA) [n^5 - 5*n^3 + 5*n: n in [1..40]]; // _Vincenzo Librandi_, Jan 11 2015

%Y Cf. A230584.

%K nonn

%O 1,2

%A _Ralf Stephan_, Oct 24 2013

%E More terms from _Vincenzo Librandi_, Jan 11 2015

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Last modified October 18 22:57 EDT 2019. Contains 328211 sequences. (Running on oeis4.)