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A127446
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Triangle T(n,k) = n*A051731(n,k) read by rows.
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5
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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, 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, 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
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OFFSET
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1,2
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COMMENTS
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Replace the 1's in row n of A051731 with n's.
T(n,k) is the sum of the k's in the partitions of n into equal parts. - Omar E. Pol, Nov 25 2019
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LINKS
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FORMULA
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EXAMPLE
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First few rows of the triangle:
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;
...
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
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MAPLE
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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
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MATHEMATICA
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Flatten[Table[If[Mod[n, k] == 0, n, 0], {n, 20}, {k, n}]] (* Vincenzo Librandi, Nov 02 2016 *)
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PROG
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(Haskell)
a127446 n k = a127446_tabl !! (n-1) !! (k-1)
a127446_row n = a127446_tabl !! (n-1)
a127446_tabl = zipWith (\v ws -> map (* v) ws) [1..] a051731_tabl
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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