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A051194
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Triangular array T read by rows: T(n,k)=number of positive integers that divide both n and k.
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1
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1, 1, 2, 1, 1, 2, 1, 2, 1, 3, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 4, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 2, 1, 4, 1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 2, 1, 2, 2, 2, 1, 2, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 3, 1, 4, 1, 3, 2, 2, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| T(n,k) = A000005(A050873(n,k)). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 28 2010]
The function T(n, k) is defined for all integer n, k but only the values for 1<=k<=n as a triangular array are listed here.
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FORMULA
| T(n, k) = T(k, n) = T(-n, k) = T(n, -k) = T(n, n+k) = T(n+k, k). Michael Somos Jul 18 2011
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EXAMPLE
| Rows: {1}; {1,2}; {1,1,2}; {1,2,1,3}; {1,1,1,1,2}; {1,2,2,2,1,4}; ...
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MATHEMATICA
| T[ n_, k_] := Length[Intersection[Divisors @ If[n == 0, 1, n], Divisors @ If[k == 0, 1, k]]] (* Michael Somos Jul 18 2011 *)
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PROG
| (PARI) {T(n, k) = sum( i=1, min( abs(n), abs(k)), (n%i == 0) && (k%i == 0))} /* Michael Somos Jul 18 2011 */
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CROSSREFS
| Sum of numbers in row n matches A000203. Sum of numbers in first n rows matches A024916.
Sequence in context: A029396 A084746 A128259 * A134838 A049843 A131374
Adjacent sequences: A051191 A051192 A051193 * A051195 A051196 A051197
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KEYWORD
| nonn,tabl
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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