A093415 - OEIS

A093415

Triangle read by rows: a(n, k) is the denominator of (n + (n-1) + ... + (n-k+1))/(1 + 2 + ... + k), 0 < k <= n.

1, 1, 1, 1, 3, 1, 1, 3, 2, 1, 1, 1, 1, 5, 1, 1, 3, 2, 5, 3, 1, 1, 3, 1, 5, 3, 7, 1, 1, 1, 2, 5, 1, 7, 4, 1, 1, 3, 1, 1, 3, 7, 2, 9, 1, 1, 3, 2, 5, 3, 7, 4, 9, 5, 1, 1, 1, 1, 5, 1, 7, 1, 3, 5, 11, 1, 1, 3, 2, 5, 3, 7, 4, 9, 5, 11, 6, 1, 1, 3, 1, 5, 3, 1, 2, 9, 5, 11, 3, 13, 1, 1, 1, 2, 1, 1, 7, 4, 3, 1, 11, 2

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OFFSET

1,5

COMMENTS

A093412 gives the corresponding numerators.

A109613(n+1) - 2 = 2*floor((n+1)/2) - 1 is the largest number in row n. [Corrected by Petros Hadjicostas, Oct 20 2019]

LINKS

Table of n, a(n) for n=1..102.

FORMULA

a(n, k) = (k+1)/gcd(2n+2, k+1).

EXAMPLE

Triangle a(n,k) (with rows n >= 1 and columns k >= 1) begins as follows: