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 A168532 Triangle read by rows, A054525 * A168021. 15
 1, 1, 1, 2, 0, 1, 3, 1, 0, 1, 6, 0, 0, 0, 1, 7, 2, 1, 0, 0, 1, 14, 0, 0, 0, 0, 0, 1, 17, 3, 0, 1, 0, 0, 0, 1, 27, 0, 2, 0, 0, 0, 0, 0, 1, 34, 6, 0, 0, 1, 0, 0, 0, 0, 1, 55, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 63, 7, 3, 2, 0, 1, 0, 0, 0, 0, 0, 1, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Row sums = A000041 starting (1, 2, 3, 5, 7, 11, 15, ...). T(n,k) is the number of partitions of n into parts with GCD = k. - Alois P. Heinz, Jun 06 2013 LINKS Alois P. Heinz, Rows n = 1..141, flattened FORMULA Mobius transform of triangle A168021 = an infinite lower triangular matrix with aerated variants of A000837 in each column; where A000837 = the Mobius transform of the partition numbers, A000041. EXAMPLE First few rows of the triangle = 1; 1,    1; 2,    0, 1; 3,    1, 0, 1; 6,    0, 0, 0,  1; 7,    2, 1, 0,  0, 1; 14,   0, 0, 0,  0, 0, 1; 17,   3, 0, 1,  0, 0, 0, 1; 27,   0, 2, 0,  0, 0, 0, 0, 1; 34,   6, 0, 0,  1, 0, 0, 0, 0, 1; 55,   0, 0, 0,  0, 0, 0, 0, 0, 0, 1; 63,   7, 3, 2,  0, 1, 0, 0, 0, 0, 0, 1; 100,  0, 0, 0,  0, 0, 0, 0, 0, 0, 0, 0, 1; 119, 14, 0, 0,  0, 0, 1, 0, 0, 0, 0, 0, 0, 1; 167,  0, 6, 0,  2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1; 209, 17, 0, 3,  0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1; 296,  0, 0, 0,  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1; ... MAPLE b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i=1, x,       b(n, i-1)+(p-> add(coeff(p, x, t)*x^igcd(t, i),       t=0..degree(p)))(add(b(n-i*j, i-1), j=1..n/i))))     end: T:= n-> (p-> seq(coeff(p, x, i), i=1..n))(b(n\$2)): seq(T(n), n=1..17);  # Alois P. Heinz, Mar 29 2015 MATHEMATICA b[n_, i_] := b[n, i] = If[n==0, 1, If[i==1, x, b[n, i-1] + Function[{p}, Sum[Coefficient[p, x, t]*x^GCD[t, i], {t, 0, Exponent[p, x]}]][Sum[b[n - i*j, i-1], {j, 1, n/i}]]]]; T[n_] := Function[{p}, Table[Coefficient[p, x, i], {i, 1, n}]][b[n, n]]; Table[T[n], {n, 1, 17}] // Flatten (* Jean-François Alcover, Jan 08 2016, after Alois P. Heinz *) CROSSREFS Cf. A168021, A000837. Cf. A256067 (the same for LCM). Sequence in context: A026794 A137712 A194711 * A181940 A261209 A340006 Adjacent sequences:  A168529 A168530 A168531 * A168533 A168534 A168535 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, Nov 28 2009 EXTENSIONS Corrected and extended by Alois P. Heinz, Jun 06 2013 STATUS approved

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Last modified December 1 01:37 EST 2021. Contains 349426 sequences. (Running on oeis4.)