A054372 Table of resultants for cyclotomic polynomials phi_k(x) and phi_n(x).

0, 2, 0, 3, 1, 0, 2, 2, 1, 0, 5, 1, 1, 1, 0, 1, 3, 4, 1, 1, 0, 7, 1, 1, 1, 1, 1, 0, 2, 2, 1, 4, 1, 1, 1, 0, 3, 1, 9, 1, 1, 1, 1, 1, 0, 1, 5, 1, 1, 16, 1, 1, 1, 1, 0, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 4, 9, 1, 4, 1, 1, 1, 1, 1, 0, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 7, 1, 1, 1, 1, 64, 1, 1

Offset

1,2

Links

T. D. Noe, Rows n=1..100 of triangle, flattened

T. M. Apostol, Resultants of cyclotomic polynomials, Proc. Amer. Math. Soc. 24 (1970), 457-462.

Eric Weisstein's World of Mathematics, Cyclotomic Polynomial.

Example

Triangle begins:
  0;
  2, 0;
  3, 1, 0;
  2, 2, 1, 0;
  5, 1, 1, 1, 0;
  1, 3, 4, 1, 1, 0;
  7, 1, 1, 1, 1, 1, 0;
  2, 2, 1, 4, 1, 1, 1, 0;
  ...

Mathematica

Flatten[Table[Resultant[Cyclotomic[n, x], Cyclotomic[k, x], x], {k, 20}, {n, k}]]

Prog

(PARI) T(n, k) = polresultant(polcyclo(k), polcyclo(n));
row(n) = vector(n, k, T(n, k)); \\ Michel Marcus, Aug 18 2021

Crossrefs

Sequence in context: A238762 A269517 A190440 * A070679 A177443 A176919

Adjacent sequences: A054369 A054370 A054371 * A054373 A054374 A054375

Keyword

nonn,easy,nice,tabl

Author

Eric W. Weisstein

Status

approved