A267864 Denominator triangle for A267863: T(n, k) = denominator((n - 2*k)/(2*n)), n >= 1, k = 1, ..., n.

2, 1, 2, 6, 6, 2, 4, 1, 4, 2, 10, 10, 10, 10, 2, 3, 6, 1, 6, 3, 2, 14, 14, 14, 14, 14, 14, 2, 8, 4, 8, 1, 8, 4, 8, 2, 18, 18, 6, 18, 18, 6, 18, 18, 2, 5, 10, 5, 10, 1, 10, 5, 10, 5, 2, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 2, 12, 3, 4, 6, 12, 1, 12, 6, 4, 3, 12, 2

Offset

1,1

Comments

For details and the Hurwitz reference see A267863.

Links

G. C. Greubel, Rows n = 1..50 of the triangle, flattened

Formula

T(n, k) = denominator((n - 2*k)/(2*n)), n >= 1, k = 1, ..., n.

Example

The triangle begins:
m\a   1   2   3   4   5   6   7   8  9  10 ...
1:    2
2:    1   2
3:    6   6   2
4:    4   1   4   2
5:   10  10  10  10   2
6:    3   6   1   6   3   2
7:   14  14  14  14  14  14   2
8:    8   4   8   1   8   4   8   2
9:   18  18   6  18  18   6  18  18  2
10:   5  10   5  10   1  10   5  10  5   2
...
For the beginning of the rational triangle R(m, a) see A267863.

Mathematica

R[m_, a_] := HurwitzZeta[0, a/m]; (* or *) R[m_, a_] := (m - 2*a)/(2*m); Table[R[m, a] // Denominator, {m, 1, 12}, {a, 1, m}] // Flatten (* Jean-François Alcover, Feb 26 2016 *)

Prog

(Magma)
A267864:= func< n, k |  Denominator((n-2*k)/(2*n)) >;
[A267864(n, k): k in [1..n], n in [1..12]]; // G. C. Greubel, Oct 04 2024
(SageMath)
def A267864(n, k): return denominator((n-2*k)/(2*n))
flatten([[A267864(n, k) for k in range(1, n+1)] for n in range(1, 13)]) # G. C. Greubel, Oct 04 2024

Crossrefs

Cf. A267863.

Sequence in context: A300769 A300639 A301361 * A336524 A219570 A285030

Adjacent sequences: A267861 A267862 A267863 * A267865 A267866 A267867

Keyword

nonn,frac,tabl,easy

Author

Wolfdieter Lang, Feb 18 2016

Status

approved