A173541 - OEIS

%I #5 Feb 19 2014 18:20:37

%S 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,

%T 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,

%U 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

%N 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).

%C 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".

%H Reinhard Zumkeller, <a href="/A173541/b173541.txt">Rows n = 1..125 of triangle, flattened</a>

%F T(n,k) = k * A051731(n,k). - _Reinhard Zumkeller_, Feb 19 2014

%e Triangle begins:

%e 0;

%e 0,0;

%e 0,2,0;

%e 0,0,3,0;

%e 0,2,3,4,0;

%e 0,0,0,4,5,0;

%e 0,2,3,4,5,6,0;

%e 0,0,3,0,5,6,7,0;

%e 0,2,0,4,5,6,7,8,0;

%e 0,0,3,4,0,6,7,8,9,0;

%e 0,2,3,4,5,6,7,8,9,10,0;

%e 0,0,0,0,5,0,7,8,9,10,11,0;

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

%e 0,0,3,4,5,6,0,8,9,10,11,12,13,0;

%e 0,2,0,4,0,6,7,8,9,10,11,12,13,14,0;

%e 0,0,3,0,5,6,7,0,9,10,11,12,13,14,15,0;

%o (Haskell)

%o a173541 n k = a173541_tabl !! (n-1) !! (n-1)

%o a173541_row n = a173541_tabl !! (n-1)

%o a173541_tabl = zipWith (zipWith (*))

%o                        a002260_tabl $ map (map (1 -)) a051731_tabl

%o -- _Reinhard Zumkeller_, Feb 19 2014

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

%Y Cf. A002260.

%K easy,nonn,tabl

%O 1,5

%A _Omar E. Pol_, May 25 2010