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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
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
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.)