%I #36 Dec 21 2022 08:19:19
%S 1,1,3,1,1,4,1,3,1,7,1,1,1,1,6,1,3,4,3,1,12,1,1,1,1,1,1,8,1,3,1,7,1,3,
%T 1,15,1,1,4,1,1,4,1,1,13,1,3,1,3,6,3,1,3,1,18,1,1,1,1,1,1,1,1,1,1,12,
%U 1,3,4,7,1,12,1,7,4,3,1,28,1,1,1,1,1,1,1,1,1,1,1,1,14,1,3,1,3,1,3,8,3,1,3,1,3,1,24
%N Triangle whose n-th row consists of the first n terms of the n-th row of A134866.
%C Previous name: Triangle, n-th row = first n terms of n-th row of an array formed by A051731 * A127093 (transform).
%C Right border = sigma(n), A000203.
%C Row sums = A038040.
%C The function T(n,k) = T(k,n) is defined for k > n, but only the values of k in 1..n as a triangular array are listed here.
%H Reinhard Zumkeller, <a href="/A132442/b132442.txt">Rows n = 1..125 of triangle, flattened</a>
%F T(n,k) = A000203(gcd(n,k)). - _Reinhard Zumkeller_, Dec 12 2015
%e First few rows of the A134866 array:
%e 1, 1, 1, 1, 1, 1, 1, ...
%e 1, 3, 1, 3, 1, 3, 1, ...
%e 1, 1, 4, 1, 1, 4, 1, ...
%e 1, 3, 1, 7, 1, 3, 1, ...
%e 1, 1, 1, 1, 6, 1, 1, ...
%e 1, 3, 4, 3, 1, 12, 1, ...
%e ...
%e First few rows of the triangle:
%e 1;
%e 1, 3;
%e 1, 1, 4;
%e 1, 3, 1, 7;
%e 1, 1, 1, 1, 6;
%e 1, 3, 4, 3, 1, 12;
%e 1, 1, 1, 1, 1, 1, 8;
%e 1, 3, 1, 7, 1, 3, 1, 15;
%e ...
%t T[ n_, k_] := If[ n < 1 || k < 1, 0, If[ k > n, T[ k, n], If[ k == 1, 1, If[ n > k, T[ k, Mod[ n, k, 1]], DivisorSigma [1, n]]]]] (* _Michael Somos_, Jul 18 2011 *)
%o (PARI) {T(n, k) = if( n<1 || k<1, 0, if( k>n, T(k, n), if( k==1, 1, if( n>k, T(k, (n-1)%k+1), sigma( n)))))} /* _Michael Somos_, Jul 18 2011 */
%o (Haskell)
%o a132442 n k = a132442_tabl !! (n-1) !! (k-1)
%o a132442_row n = a132442_tabl !! (n-1)
%o a132442_tabl = map (map a000203) a050873_tabl
%o -- _Reinhard Zumkeller_, Dec 12 2015
%Y Cf. A051731, A127093.
%Y Cf. A038040 (row sums), A000203 (right border), A050873 (gcd(n,k)).
%Y Cf. A000142 (determinant).
%Y Cf. A134866.
%K nonn,tabl
%O 1,3
%A _Gary W. Adamson_, Nov 14 2007
%E Missing T(10,9) = 1 inserted by _Reinhard Zumkeller_, Dec 12 2015
%E Name edited by _Michel Marcus_, Dec 21 2022