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A050873
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Triangular array T read by rows: T(u,v)=GCD(u,v).
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24
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| a(n)=GCD(A002260(n),A002024(n)); A054521(n)=A000007(a(n)). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 02 2009]
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.
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LINKS
| T. D. Noe, Rows n=1..100, flattened
Eric Weisstein's World of Mathematics, Greatest Common Divisor
Wikipedia, Greatest Common Divisor
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FORMULA
| T(n,k) = A075362(n,k)/A051173(n,k), 1<=k<=n. [Reinhard Zumkeller, Apr 25 2011]
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}; (1,1,3}; {1,2,1,4}; {1,1,1,1,5}; {1,2,3,2,1,6}; ...
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MATHEMATICA
| ColumnForm[Table[GCD[n, k], {k, 12}, {n, k}], Center] (* From Alonso del Arte, Jan 14 2011 *)
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PROG
| (PARI) {T(n, k) = gcd(n, k)} /* Michael Somos Jul 18 2011 */
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CROSSREFS
| Cf. A003989.
Sequence in context: A107359 A112377 A127704 * A128221 A175488 A115758
Adjacent sequences: A050870 A050871 A050872 * A050874 A050875 A050876
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KEYWORD
| nonn,tabl
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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