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A027446 Square of the lower triangular mean matrix. 9
1, 3, 1, 11, 5, 2, 25, 13, 7, 3, 137, 77, 47, 27, 12, 147, 87, 57, 37, 22, 10, 1089, 669, 459, 319, 214, 130, 60, 2283, 1443, 1023, 743, 533, 365, 225, 105, 7129, 4609, 3349, 2509, 1879, 1375, 955, 595, 280, 7381, 4861, 3601, 2761, 2131, 1627, 1207, 847 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The rational matrix A^2, where the matrix A has elements a[i,j] = 1/A002024(i,j) is equal to A119947(i,j)/A119948(i,j).

LINKS

Table of n, a(n) for n=1..53.

FORMULA

Numerators of lower triangle of (a[ i, j ])^2 where a[ i, j ] = 1/i if j<=i, 0 if j>i.

a(i,j) = lcm(seq(A119948(i,m),m=1..i))*A119947(i,j)/A119948(i,j), 1 <= j =< i and zero otherwise.

EXAMPLE

Triangle starts

     1

     3,    1

    11,    5,    2

    25,   13,    7,    3

   137,   77,   47,   27,   12

   147,   87,   57,   37,   22,   10

  1089,  669,  459,  319,  214,  130,  60

  2283, 1443, 1023,  743,  533,  365, 225, 105

  7129, 4609, 3349, 2509, 1879, 1375, 955, 595, 280

  ... - Joerg Arndt, Mar 29 2013

MATHEMATICA

rows = 10; m = Table[ If[j <= i, 1/i, 0], {i, 1, rows}, {j, 1, rows}]; m2 = m.m; Table[fracs = m2[[i]]; nums = fracs // Numerator; dens = fracs // Denominator; lcm = LCM @@ dens; Table[ nums[[j]]*lcm/dens[[j]], {j, 1, i}], {i, 1, rows}] // Flatten (* Jean-François Alcover, Mar 05 2013 *)

CROSSREFS

The row sums give A081528(n), n>=1.

The column sequences give A025529, A027457, A027458 for j=1..3.

The diagonal sequences give A002944, A027449, A027450.

Cf. A027447, A027448.

Sequence in context: A099001 A119947 A165674 * A027516 A092808 A113955

Adjacent sequences:  A027443 A027444 A027445 * A027447 A027448 A027449

KEYWORD

nonn,tabl

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified May 19 21:29 EDT 2019. Contains 323410 sequences. (Running on oeis4.)