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A248667 Numbers k for which coefficients of the polynomial p(k,x) defined in Comments are relatively prime. 6
1, 3, 7, 9, 11, 17, 19, 21, 23, 27, 29, 31, 33, 41, 43, 47, 49, 51, 53, 57, 59, 61, 63, 67, 69, 71, 73, 77, 79, 81, 83, 87, 89, 93, 97, 99, 101, 103, 107, 109, 113, 119, 121, 123, 127, 129, 131, 133, 137, 139, 141, 147, 149, 151, 153, 157, 159, 161, 163, 167 (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.

LINKS

Table of n, a(n) for n=1..60.

EXAMPLE

The first six polynomials with GCD(coefficients) shown just to the right of "=":

p(1,x) = 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 a(1) = 1 and a(2) = 3.

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 *)

u = Table[Apply[GCD, c[n]], {n, 1, 60}]  (* A248666 *)

Flatten[Position[u, 1]]  (* A248667 *)

Table[Apply[Plus, c[n]], {n, 1, 60}] (* A248668 *)

CROSSREFS

Cf. A248664, A248665, A248666, A248668, A248669.

Sequence in context: A287914 A291348 A186890 * A075607 A256465 A275386

Adjacent sequences:  A248664 A248665 A248666 * A248668 A248669 A248670

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Oct 11 2014

STATUS

approved

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Last modified November 18 02:07 EST 2019. Contains 329242 sequences. (Running on oeis4.)