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A326933 Number of nonconstant irreducible polynomial divisors of the n-th polynomial given in A326926.

%I A326933 #13 Mar 14 2023 18:31:36
%S A326933 0,1,2,2,1,5,1,3,4,3,1,8,1,3,5,4,1,9,1,5,5,3,1,11,2,3,6,5,1,11,1,5,5,
%T A326933 3,3,14,1,3,5,7,1,11,1,5,9,3,1,14,2,5,5,5,1,13,3,7,5,3,1,17,1,3,9,6,3,
%U A326933 11,1,5,5,7,1,19,1,3,8,5,3,11,1,9,8,3,1
%N A326933 Number of nonconstant irreducible polynomial divisors of the n-th polynomial given in A326926.
%C A326933 It appears that each nonconstant polynomial is irreducible if and only if its degree is p-1 for some prime p other than 3.
%H A326933 Antti Karttunen, <a href="/A326933/b326933.txt">Table of n, a(n) for n = 0..2048</a>
%e A326933 The 5 nonconstant irreducible divisors of the 5th polynomial appear in this factorization: -3 x (-2 + x) (-1 + x) (1 + x) (-1 + 2 x).
%t A326933 g[x_, n_] := Numerator[ Factor[D[1/(x^2 - x + 1), {x, n}]]];
%t A326933 Column[Expand[Table[g[x, n]/n!, {n, 0, 12}]]] (* polynomials *)
%t A326933 h[n_] := CoefficientList[g[x, n]/n!, x]
%t A326933 Table[h[n], {n, 0, 10}]
%t A326933 Column[%]  (* A326926 array *)
%t A326933 Table[-1 + Length[FactorList[g[x, n]/n!]], {n, 0, 100}]  (* A326933 *)
%o A326933 (PARI) A326933(n) = { my(p=1/(1-x+x^2)); for(k=1,n, p = deriv(p)); #(factor(numerator(p)/n!)~); };
%Y A326933 Cf. A326926.
%K A326933 nonn
%O A326933 0,3
%A A326933 _Clark Kimberling_, Nov 01 2019
%E A326933 Starting offset corrected from 1 to 0 by _Antti Karttunen_, Mar 02 2023