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A248666 Greatest common divisor of the coefficients of the polynomial p(n,x) defined in Comments. 7
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 (list; graph; refs; listen; history; text; internal format)
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: A264017 A159971 A114158 * A162407 A132741 A072436

Adjacent sequences:  A248663 A248664 A248665 * A248667 A248668 A248669

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Oct 11 2014

STATUS

approved

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Last modified May 11 16:45 EDT 2021. Contains 343804 sequences. (Running on oeis4.)