A173541 Triangle read by rows: T(n,k)=k if k is a proper non-divisor of n, otherwise T(n,k)=0 (1<=k<=n).

0, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 2, 3, 4, 0, 0, 0, 0, 4, 5, 0, 0, 2, 3, 4, 5, 6, 0, 0, 0, 3, 0, 5, 6, 7, 0, 0, 2, 0, 4, 5, 6, 7, 8, 0, 0, 0, 3, 4, 0, 6, 7, 8, 9, 0, 0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 0, 0, 0, 0, 5, 0, 7, 8, 9, 10, 11, 0, 0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 0, 0, 3, 4, 5, 6, 0, 8, 9, 10, 11

Offset: 1

Author

Omar E. Pol, May 25 2010

Keywords

• easy
• nonn
• tabl

Comments

Observation: Note that the k-th column is a sequence where the periodic subset is formed by zero together with k-1 numbers k. For example, the 5th column can be defined as "Period 5: repeat 0,5,5,5,5".

Examples

			Triangle begins:
0;
0,0;
0,2,0;
0,0,3,0;
0,2,3,4,0;
0,0,0,4,5,0;
0,2,3,4,5,6,0;
0,0,3,0,5,6,7,0;
0,2,0,4,5,6,7,8,0;
0,0,3,4,0,6,7,8,9,0;
0,2,3,4,5,6,7,8,9,10,0;
0,0,0,0,5,0,7,8,9,10,11,0;
0,2,3,4,5,6,7,8,9,10,11,12,0;
0,0,3,4,5,6,0,8,9,10,11,12,13,0;
0,2,0,4,0,6,7,8,9,10,11,12,13,14,0;
0,0,3,0,5,6,7,0,9,10,11,12,13,14,15,0;
		

Links

• Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

Crossrefs

Cf. A049820, A127093, A173540. Row sums give A024816.

Cf. A002260.

Programs

Haskell

a173541 n k = a173541_tabl !! (n-1) !! (n-1)
a173541_row n = a173541_tabl !! (n-1)
a173541_tabl = zipWith (zipWith (*))
                       a002260_tabl $ map (map (1 -)) a051731_tabl
-- Reinhard Zumkeller, Feb 19 2014

Formula

T(n,k) = k * A051731(n,k). - Reinhard Zumkeller, Feb 19 2014