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A050873 Triangular array T read by rows: T(u,v)=GCD(u,v). 26
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; text; internal format)
OFFSET

1,3

COMMENTS

a(n)=GCD(A002260(n),A002024(n)); A054521(n)=A000007(a(n)). [From Reinhard Zumkeller, 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.

LINKS

T. D. Noe, Rows n=1..100, flattened

Eric Weisstein's World of Mathematics, Greatest Common Divisor

Wikipedia, Greatest Common Divisor

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

T(n,k) = A051173(n,k) / A051537(n,k). Reinhard Zumkeller, Jul 07 2013

EXAMPLE

Rows:

1;

1,2;

1,1,3;

1,2,1,4;

1,1,1,1,5;

1,2,3,2,1,6; ...

MATHEMATICA

ColumnForm[Table[GCD[n, k], {k, 12}, {n, k}], Center] (* From Alonso del Arte, Jan 14 2011 *)

PROG

(PARI) {T(n, k) = gcd(n, k)} /* Michael Somos Jul 18 2011 */

(Haskell)

a050873 = gcd

a050873_row n = a050873_tabl !! (n-1)

a050873_tabl = map (\x -> map (gcd x) [1..x]) [1..]

-- Reinhard Zumkeller, Aug 13 2013, Jun 10 2013

CROSSREFS

Cf. A003989.

Cf. A002262, A054531, A226314.

Sequence in context: A107359 A112377 A127704 * A128221 A175488 A115758

Adjacent sequences:  A050870 A050871 A050872 * A050874 A050875 A050876

KEYWORD

nonn,tabl,look

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified April 23 14:18 EDT 2014. Contains 240931 sequences.