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A132442
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Triangle, n-th row = first n terms of n-th row of an array formed by A051731 * A127093(transform).
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3
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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, 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, 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
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OFFSET
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1,3
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COMMENTS
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Right border = sigma(n), A000203.
Row sums = A038040.
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.
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LINKS
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Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened
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FORMULA
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Given an array formed by A051731 * A127093(transform), extract the first n terms of row n to form the triangle.
T(n,k) = A000203(gcd(n,k)). - Reinhard Zumkeller, Dec 12 2015
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EXAMPLE
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First few rows of the array:
1, 1, 1, 1, 1, 1, 1, ...
1, 3, 1, 3, 1, 3, 1, ...
1, 1, 4, 1, 1, 4, 1, ...
1, 3, 1, 7, 1, 3, 1, ...
1, 1, 1, 1, 6, 1, 1, ...
1, 3, 4, 3, 1, 12, 1, ...
...
First few rows of the triangle:
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, 1, 15;
...
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MATHEMATICA
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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 *)
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PROG
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(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 */
(Haskell)
a132442 n k = a132442_tabl !! (n-1) !! (k-1)
a132442_row n = a132442_tabl !! (n-1)
a132442_tabl = map (map a000203) a050873_tabl
-- Reinhard Zumkeller, Dec 12 2015
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CROSSREFS
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Cf. A051731, A127093, A038040 (row sums), A000203 (right border).
Cf. A050873.
Sequence in context: A284373 A104610 A138684 * A074927 A139605 A191780
Adjacent sequences: A132439 A132440 A132441 * A132443 A132444 A132445
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson, Nov 14 2007
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EXTENSIONS
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Missing T(10,9) = 1 inserted by Reinhard Zumkeller, Dec 12 2015
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STATUS
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approved
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