A051194 Triangular array T read by rows: T(n,k) = number of positive integers that divide both n and k.

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

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