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 A119947 Triangle of numerators in the square of the matrix A[i,j] = 1/i for j <= i, 0 otherwise. 5
 1, 3, 1, 11, 5, 1, 25, 13, 7, 1, 137, 77, 47, 9, 1, 49, 29, 19, 37, 11, 1, 363, 223, 153, 319, 107, 13, 1, 761, 481, 341, 743, 533, 73, 15, 1, 7129, 4609, 3349, 2509, 1879, 275, 191, 17, 1, 7381, 4861, 3601, 2761, 2131, 1627, 1207, 121, 19, 1, 83711, 55991, 42131, 32891, 25961 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The triangle of the corresponding denominators is A119948. The rationals appear in lowest terms (while in A027446 they are row-wise on the least common denominator). The triangle with row number i multiplied with the least common multiple (LCM) of its denominators yields A027446. First column is A001008. - Tilman Neumann, Oct 01 2008 Column 2 is A064169. - Clark Kimberling, Aug 13 2012 Third diagonal (11, 13, 47, ...) is A188386. - Clark Kimberling, Aug 13 2012 LINKS Wolfdieter Lang, First ten rows and rationals. FORMULA a(i,j) = numerator(r(i,j)) with r(i,j):=(A^2)[i,j], where the matrix A has elements a[i,j] = 1/i if j<=i, 0 if j>i, (lower triangular). EXAMPLE The rationals are ; [3/4, 1/4]; [11/18, 5/18, 1/9]; [25/48, 13/48, 7/48, 1/16]; ... See the W. Lang link for more. From Clark Kimberling, Aug 13 2012: (Start) As a triangle given by f(n,m) = Sum_{h=m..n} 1/h, the first six rows are:     1     3    1    11    5    1    25   13    7    1   137   77   47    9    1    49   29   19   37   11    1   363  223  153  319  107   13    1 (End) MATHEMATICA f[n_, m_] := Numerator[Sum[1/k, {k, m, n}]] Flatten[Table[f[n, m], {n, 1, 10}, {m, 1, n}]] TableForm[Table[f[n, m], {n, 1, 10}, {m, 1, n}]] (* Clark Kimberling, Aug 13 2012 *) PROG (PARI) A119947_upto(n)={my(M=matrix(n, n, i, j, (j<=i)/i)^2); vector(n, r, apply(numerator, M[r, 1..r]))} \\ M. F. Hasler, Nov 05 2019 CROSSREFS Cf. A002024: i appears i times (denominators in row i of the matrix A). Row sums give A119949. Row sums of the triangle of rationals always give 1. For the cube of this matrix see the rational triangle A119935/A119932 and A027447; see A027448 for the fourth power. Cf. A001008, A027446, A064169, A119948, A188386. Sequence in context: A229834 A120291 A099001 * A165674 A027446 A027516 Adjacent sequences:  A119944 A119945 A119946 * A119948 A119949 A119950 KEYWORD nonn,easy,frac,tabl AUTHOR Wolfdieter Lang, Jul 20 2006 EXTENSIONS Edited by M. F. Hasler, Nov 05 2019 STATUS approved

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Last modified April 18 12:45 EDT 2021. Contains 343088 sequences. (Running on oeis4.)