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 A244840 Denominators of the triangle T(n,k) = (n*(n+1)/2+k+1)/(k+1) for n >= k >= 0. 1
 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 2, 1, 4, 1, 2, 1, 2, 1, 4, 5, 2, 1, 1, 1, 3, 1, 5, 3, 1, 2, 1, 1, 1, 1, 5, 1, 7, 2, 1, 1, 2, 1, 4, 1, 2, 7, 8, 1, 2, 1, 2, 3, 4, 1, 6, 7, 8, 9, 2, 1, 1, 1, 1, 2, 5, 1, 7, 4, 3, 5, 1, 2 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Numerators: A244734(n,k). See A244734 for the first entries of the rational triangle T(n,k). LINKS FORMULA a(n,k) = denominator((n*(n+1)/2 + k + 1)/(k+1)) for n >= k >= 0. EXAMPLE T(0,0) = 1/1, T(1,0) = 2/1, T(1,1) = 3/2,... . The triangle a(n,k) begins: n/k  0 1 2 3 4 5 6 7 8  9 10 11 12 13 14 15 16 17 18 19 20 ... 0:   1 1:   1 2 2:   1 2 1 3:   1 1 1 2 4:   1 1 3 2 1 5:   1 2 1 4 1 2 6:   1 2 1 4 5 2 1 7:   1 1 3 1 5 3 1 2 8:   1 1 1 1 5 1 7 2 1 9:   1 2 1 4 1 2 7 8 1  2 10:  1 2 3 4 1 6 7 8 9  2  1 11:  1 1 1 2 5 1 7 4 3  5  1  2 12:  1 1 1 2 5 1 7 4 3  5 11  2 1 13:  1 2 3 4 5 6 1 8 9 10 11 12 1   2 14:  1 2 1 4 1 2 1 8 3  2 11  4 13  2  1 15:  1 1 1 1 1 1 7 1 3  1 11  1 13  7  1  2 16:  1 1 3 1 5 3 7 1 9  5 11  3 13  7 15  2  1 17:  1 2 1 4 5 2 7 8 1 10 11  4 13 14  5 16  1  2 18:  1 2 1 4 5 2 7 8 1 10 11  4 13 14  5 16 17  2  1 19:  1 1 3 2 1 3 7 4 9  1 11  6 13  7  3  8 17  9  1  2 20:  1 1 1 2 1 1 1 4 3  1 11  2 13  1  1  8 17  3 19  2  1 n/k  0 1 2 3 4 5 6 7 8  9 10 11 12 13 14 15 16 17 18 19 20 ... .. reformatted - Wolfdieter Lang, Jul 28 2014 . The second column is of period 4: repeat 2, 2, 1, 1. From A014695 or A130658. The third column is of period 3: repeat 1, 1, 3. From A109007. The fourth column is of period 8: repeat 2, 2, 4, 4, 1, 1, 4, 4. The fifth column is of period 5: repeat 1, 1, 5, 5, 5. The sixth column is of period 12: repeat 2, 2, 3, 1, 2, 6, 1, 1, 6, 2, 1, 3 . The seventh column is of period 7: repeat 1, 1, 7, 7, 7, 7, 7. Hence the positive terms of A022998. Main diagonal: A000034(n). Alternate main and second diagonal: A130658(n). Common denominator by row: 1, 2, 2, 2, 6, 4, 20, 30, 70, ... . MATHEMATICA Table[(n*(n+1)/2+k+1)/(k+1) // Denominator, {n, 0, 11}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jul 08 2014 *) CROSSREFS Cf. A014695, A130658, A109007, A002260, A022998, A244734, A000034. Sequence in context: A156144 A136044 A184240 * A103414 A092400 A303598 Adjacent sequences:  A244837 A244838 A244839 * A244841 A244842 A244843 KEYWORD nonn,frac,tabl,easy AUTHOR Paul Curtz, Jul 07 2014 EXTENSIONS Editse: Name reformulated, comment with T(n,k) reference added. - Wolfdieter Lang, Jul 28 2014 STATUS approved

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Last modified August 3 13:22 EDT 2021. Contains 346438 sequences. (Running on oeis4.)