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A050873
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Triangular array T read by rows: T(n,k) = gcd(n,k).
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44
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1, 1, 2, 1, 1, 3, 1, 2, 1, 4, 1, 1, 1, 1, 5, 1, 2, 3, 2, 1, 6, 1, 1, 1, 1, 1, 1, 7, 1, 2, 1, 4, 1, 2, 1, 8, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 2, 1, 2, 5, 2, 1, 2, 1, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 2, 3, 4, 1, 6, 1, 4, 3, 2, 1, 12, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
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OFFSET
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1,3
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COMMENTS
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The function T(n,k) = T(k,n) is defined for all integer k,n but only the values for 1 <= k <= n as a triangular array are listed here.
For each divisor d of n, the number of d's in row n is phi(n/d). Furthermore, if {a_1, a_2, ..., a_phi(n/d)} is the set of positive integers <= n/d that are relatively prime to n/d then T(n,a_i * d) = d. - Geoffrey Critzer, Feb 22 2015
Starting with any row n and working downwards, consider the infinite rectangular array with k = 1..n. A repeating pattern occurs every A003418(n) rows. For example, n=3: A003418(3) = 6. The 6-row pattern starting with row 3 is {1,1,3}, {1,2,1}, {1,1,1}, {1,2,3}, {1,1,1}, {1,2,1}, and this pattern repeats every 6 rows, i.e., starting with rows {9,15,21,27,...}. - Bob Selcoe and Jamie Morken, Aug 02 2017
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LINKS
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FORMULA
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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
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Rows:
1;
1, 2;
1, 1, 3;
1, 2, 1, 4;
1, 1, 1, 1, 5;
1, 2, 3, 2, 1, 6; ...
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MATHEMATICA
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ColumnForm[Table[GCD[n, k], {k, 12}, {n, k}], Center] (* Alonso del Arte, Jan 14 2011 *)
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PROG
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(Haskell)
a050873 = gcd
a050873_row n = a050873_tabl !! (n-1)
a050873_tabl = zipWith (map . gcd ) [1..] a002260_tabl
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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