A248666 Greatest common divisor of the coefficients of the polynomial p(n,x) defined in Comments.

1, 2, 1, 4, 5, 2, 1, 4, 1, 10, 1, 4, 13, 2, 5, 4, 1, 2, 1, 20, 1, 2, 1, 4, 5, 26, 1, 4, 1, 10, 1, 4, 1, 2, 5, 4, 37, 2, 13, 20, 1, 2, 1, 4, 5, 2, 1, 4, 1, 10, 1, 52, 1, 2, 5, 4, 1, 2, 1, 20, 1, 2, 1, 4, 65, 2, 1, 4, 1, 10, 1, 4, 1, 74, 5, 4, 1, 26, 1, 20, 1

Offset

1,2

Comments

The polynomial p(n,x) is defined as the numerator when the sum 1 + 1/(n*x + 1) + 1/((n*x + 1)(n*x + 2)) + ... + 1/((n*x + 1)(n*x + 2)...(n*x + n - 1)) is written as a fraction with denominator (n*x + 1)(n*x + 2)...(n*x + n - 1). For more, see A248664. For n such that the coefficients of p(n,x) are relatively prime, see A248667.

Links

Table of n, a(n) for n=1..81.

Example

The first six polynomials are shown here.  The number just to the right of "=" is the GCD of the coefficients.
p(1,x) = 1*1
p(2,x) = 2*(x + 1)
p(3,x) = 1*(9x^2 + 12 x +  5)
p(4,x) = 4*(16 x^3 + 28 x^2 + 17 x + 4)
p(5,x) = 5*(125 x^4 + 275 x^3 + 225 x^2 + 84 x + 13)
p(6,x) = 2*(3888 x^5 + 10368 x^4 + 10800 x^3 + 5562 x^2 + 1455 x + 163), so that A248666 = (1,2,1,4,5,2, ...).

Mathematica

t[x_, n_, k_] := t[x, n, k] = Product[n*x + n - i, {i, 1, k}];
p[x_, n_] := Sum[t[x, n, k], {k, 0, n - 1}];
TableForm[Table[Factor[p[x, n]], {n, 1, 6}]]
c[n_] := c[n] = CoefficientList[p[x, n], x];
TableForm[Table[c[n], {n, 1, 10}]]   (* A248664 array *)
Table[Apply[GCD, c[n]], {n, 1, 60}]  (* A248666 *)

Crossrefs

Cf. A248664, A248665, A248667, A248668, A248669.

Sequence in context: A159971 A114158 A370181 * A162407 A368608 A352458

Adjacent sequences: A248663 A248664 A248665 * A248667 A248668 A248669

Keyword

nonn,easy

Author

Clark Kimberling, Oct 11 2014

Status

approved