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A051194 Triangular array T read by rows: T(n,k) = number of positive integers that divide both n and k. 2
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; text; internal format)
OFFSET

1,3

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..93.

Math StackExchange, A question on the discrete Fourier Transform of some function

FORMULA

T(n,k) = A000005(A050873(n,k)). - Reinhard Zumkeller, Jun 28 2010

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

EXAMPLE

Triangle begins:

{1};

{1,2};

{1,1,2};

{1,2,1,3};

{1,1,1,1,2};

{1,2,2,2,1,4};

...

MATHEMATICA

T[ n_, k_] := Length[Intersection[Divisors @ If[n == 0, 1, n], Divisors @ If[k == 0, 1, k]]] (* Michael Somos, Jul 18 2011 *)

PROG

(PARI) {T(n, k) = sum( i=1, min( abs(n), abs(k)), (n%i == 0) && (k%i == 0))} /* Michael Somos, Jul 18 2011 */

CROSSREFS

Cf. A050873 (gcd), A000005 (number of divisors), A077478 (as square array).

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

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified December 3 09:50 EST 2022. Contains 358517 sequences. (Running on oeis4.)