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A127446 Triangle T(n,k) = n*A051731(n,k) read by rows. 5

%I

%S 1,2,2,3,0,3,4,4,0,4,5,0,0,0,5,6,6,6,0,0,6,7,0,0,0,0,0,7,8,8,0,8,0,0,

%T 0,8,9,0,9,0,0,0,0,0,9,10,10,0,0,10,0,0,0,0,10,11,0,0,0,0,0,0,0,0,0,

%U 11,12,12,12,12,0,12,0,0,0,0,0,12,13,0,0,0,0,0,0,0,0,0,0,0,13,14,14,0,0,0,0,14

%N Triangle T(n,k) = n*A051731(n,k) read by rows.

%C Replace the 1's in row n of A051731 with n's.

%C T(n,k) is the sum of the k's in the partitions of n into equal parts. - _Omar E. Pol_, Nov 25 2019

%H Reinhard Zumkeller, <a href="/A127446/b127446.txt">Rows n = 1..125 of triangle, flattened</a>

%F T(n,k) = k*A126988(n,k). - _Omar E. Pol_, Nov 25 2019

%e First few rows of the triangle:

%e 1;

%e 2, 2;

%e 3, 0, 3;

%e 4, 4, 0, 4;

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

%e 6, 6, 6, 0, 0, 6;

%e 7, 0, 0, 0, 0, 0, 7;

%e ...

%e For n = 6 the partitions of 6 into equal parts are [6], [3,3], [2,2,2], [1,1,1,1,1,1], so the sum of the k's are [6, 6, 6, 0, 0, 6] respectively, equaling the 6th row of triangle. - _Omar E. Pol_, Nov 25 2019

%p A127446 := proc(n,k) if n mod k = 0 then n; else 0; fi; end: for n from 1 to 20 do for k from 1 to n do printf("%d,",A127446(n,k)) ; od: od: # _R. J. Mathar_, May 08 2009

%t Flatten[Table[If[Mod[n, k] == 0, n, 0], {n, 20}, {k, n}]] (* _Vincenzo Librandi_, Nov 02 2016 *)

%o (Haskell)

%o a127446 n k = a127446_tabl !! (n-1) !! (k-1)

%o a127446_row n = a127446_tabl !! (n-1)

%o a127446_tabl = zipWith (\v ws -> map (* v) ws) [1..] a051731_tabl

%o -- _Reinhard Zumkeller_, Jan 21 2014

%Y Cf. A038040 (row sums), A051731, A126988, A244051, A328362.

%K nonn,tabl,easy

%O 1,2

%A _Gary W. Adamson_, Jan 14 2007

%E Edited and extended by _R. J. Mathar_, May 08 2009

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Last modified July 25 02:38 EDT 2021. Contains 346276 sequences. (Running on oeis4.)