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 A027446 Triangle read by rows: square of the lower triangular mean matrix. 10
 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 Numerators of nonzero elements of A^2, written as rows using the least common denominator, where A[i,j] = 1/i if j <= i, 0 if j > i. [Edited by M. F. Hasler, Nov 05 2019] LINKS FORMULA 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). 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 *) PROG (PARI) A027446_upto(n)={my(M=matrix(n, n, i, j, (j<=i)/i)^2); vector(n, r, M[r, 1..r]*denominator(M[r, 1..r]))} \\ M. F. Hasler, Nov 05 2019 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 EXTENSIONS Edited by M. F. Hasler, Nov 05 2019 STATUS approved

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Last modified November 30 15:55 EST 2020. Contains 338807 sequences. (Running on oeis4.)