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 A326933 Number of nonconstant irreducible polynomial divisors of the n-th polynomial given in A326926. 3
 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, 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, 11, 1, 5, 5, 7, 1, 19, 1, 3, 8, 5, 3, 11, 1, 9, 8, 3, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS It appears that each nonconstant polynomial is irreducible if and only if its degree is p-1 for some prime p other than 3. LINKS Antti Karttunen, Table of n, a(n) for n = 0..2048 EXAMPLE The 5 nonconstant irreducible divisors of the 5th polynomial appear in this factorization: -3 x (-2 + x) (-1 + x) (1 + x) (-1 + 2 x). MATHEMATICA g[x_, n_] := Numerator[ Factor[D[1/(x^2 - x + 1), {x, n}]]]; Column[Expand[Table[g[x, n]/n!, {n, 0, 12}]]] (* polynomials *) h[n_] := CoefficientList[g[x, n]/n!, x] Table[h[n], {n, 0, 10}] Column[%] (* A326926 array *) Table[-1 + Length[FactorList[g[x, n]/n!]], {n, 0, 100}] (* A326933 *) PROG (PARI) A326933(n) = { my(p=1/(1-x+x^2)); for(k=1, n, p = deriv(p)); #(factor(numerator(p)/n!)~); }; CROSSREFS Cf. A326926. Sequence in context: A010243 A332963 A203953 * A123398 A277495 A188945 Adjacent sequences: A326930 A326931 A326932 * A326934 A326935 A326936 KEYWORD nonn AUTHOR Clark Kimberling, Nov 01 2019 EXTENSIONS Starting offset corrected from 1 to 0 by Antti Karttunen, Mar 02 2023 STATUS approved

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Last modified April 14 20:39 EDT 2024. Contains 371667 sequences. (Running on oeis4.)