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A050873 Triangular array T read by rows: T(u,v) = GCD(u,v). 30
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)). - 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.

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

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] (* 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 = zipWith (map . gcd ) [1..] a002260_tabl

-- Reinhard Zumkeller, Dec 12 2015, Aug 13 2013, Jun 10 2013

CROSSREFS

Cf. A003989.

Cf. A002262, A054531, A226314.

Cf. A018804 (row sums), A245717.

Cf. A132442 (sums of divisors).

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 August 29 10:01 EDT 2016. Contains 275941 sequences.