A268916 Denominators of the rational number triangle R(m, a) = -(m^2 - 6*m*a + a^2)/(12*m), m >= 1, a = 1, ..., m.

12, 12, 6, 12, 12, 4, 24, 6, 24, 3, 60, 60, 60, 60, 12, 12, 6, 4, 6, 12, 2, 84, 84, 84, 84, 84, 84, 12, 48, 12, 48, 3, 48, 12, 48, 3, 36, 36, 4, 36, 36, 4, 36, 36, 4, 60, 30, 60, 30, 12, 30, 60, 30, 60, 6, 132, 132, 132, 132, 132, 132, 132, 132, 132, 132, 12, 24, 6, 8, 3, 24, 2, 24, 3, 8, 6, 24, 1

Offset

1,1

Comments

For the numerators see A268915.

For details and the Hurwitz reference see A267863.

Links

Table of n, a(n) for n=1..78.

Formula

T(m, a) = denominator(R(m, a)) with R(m, a) = -(m^2 - 6*m*a + a^2)/(12*m), m >= 1, a = 1, ..., m.

Example

The triangle T(m, a) begins:
m\a   1   2   3   4   5   6   7   8   9  10  11
1:   12
2:   12   6
3:   12  12   4
4:   24   6  24   3
5:   60  60  60  60  12
6:   12   6   4   6  12   2
7:   84  84  84  84  84  84  12
8:   48  12  48   3  48  12  48   3
9:   36  36   4  36  36   4  36  36   4
10:  60  30  60  30  12  30  60  30  60   6
11: 132 132 132 132 132 132 132 132 132 132 12
12:  24   6   8   3  24   2  24   3   8   6  24  1
...
For the triangle of the rationals R(m, a) see A268915.

Crossrefs

Cf. A268915.

Sequence in context: A133208 A118877 A112124 * A362236 A069873 A129498

Adjacent sequences: A268913 A268914 A268915 * A268917 A268918 A268919

Keyword

nonn,frac,tabl,easy

Author

Wolfdieter Lang, Feb 18 2016

Status

approved