This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A126988 #60 Sep 08 2022 08:45:29
%S A126988 1,2,1,3,0,1,4,2,0,1,5,0,0,0,1,6,3,2,0,0,1,7,0,0,0,0,0,1,8,4,0,2,0,0,
%T A126988 0,1,9,0,3,0,0,0,0,0,1,10,5,0,0,2,0,0,0,0,1,11,0,0,0,0,0,0,0,0,0,1,12,
%U A126988 6,4,3,0,2,0,0,0,0,0,1
%N A126988 Triangle read by rows: T(n,k) = n/k if k is a divisor of n; T(n,k) = 0 if k is not a divisor of n (1 <= k <= n).
%C A126988 Row sums = A000203, sigma(n).
%C A126988 k-th column (k=0,1,2,...) is (1,2,3,...) interspersed with n consecutive zeros starting after the "1".
%C A126988 The nonzero entries of row n are the divisors of n in decreasing order. - _Emeric Deutsch_, Jan 17 2007
%C A126988 Alternating row sums give A000593. - _Omar E. Pol_, Feb 11 2018
%C A126988 T(n,k) is the number of k's in the partitions of n into equal parts. - _Omar E. Pol_, Nov 25 2019
%D A126988 David Wells, "Prime Numbers, the Most Mysterious Figures in Math", John Wiley & Sons, Inc, 2005, Appendix B.
%H A126988 Reinhard Zumkeller, <a href="/A126988/b126988.txt">Rows n = 1..125 of triangle, flattened</a>
%F A126988 From _Emeric Deutsch_, Jan 17 2007: (Start)
%F A126988 G.f. of column k: z^k/(1-z^k)^2 (k=1,2,...).
%F A126988 G.f.: G(t,z) = Sum_{k>=1} t^k*z^k/(1-z^k)^2. (End)
%F A126988 G.f.: F(x,z) = log(1/(Product_{n >= 1} (1 - x*z^n))) = Sum_{n >= 1} (x*z)^n/(n*(1 - z^n)) = x*z + (2*x + x^2)*z^2/2 + (3*x + x^3)*z^3/3 + .... Note, exp(F(x,z)) is a g.f. for A008284 (with an additional term T(0,0) equal to 1). - _Peter Bala_, Jan 13 2015
%F A126988 T(n,k) = A010766(n,k)*A051731(n,k), k=1..n. - _Reinhard Zumkeller_, Jan 20 2014
%e A126988 First few rows of the triangle are:
%e A126988 1;
%e A126988 2, 1;
%e A126988 3, 0, 1;
%e A126988 4, 2, 0, 1;
%e A126988 5, 0, 0, 0, 1;
%e A126988 6, 3, 2, 0, 0, 1;
%e A126988 7, 0, 0, 0, 0, 0, 1;
%e A126988 8, 4, 0, 2, 0, 0, 0, 1;
%e A126988 9, 0, 3, 0, 0, 0, 0, 0, 1;
%e A126988 10, 5, 0, 0, 2, 0, 0, 0, 0, 1;
%e A126988 ...
%e A126988 sigma(12) = A000203(n) = 28.
%e A126988 sigma(12) = 28, from 12th row = (12 + 6 + 4 + 3 + 2 + 1), deleting the zeros, from left to right.
%e A126988 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 number of k's are [6, 3, 2, 0, 0, 1] respectively, equaling the 6th row of triangle. - _Omar E. Pol_, Nov 25 2019
%p A126988 A126988:=proc(n,k) if type(n/k, integer)=true then n/k else 0 fi end: for n from 1 to 12 do seq(A126988(n,k),k=1..n) od; # yields sequence in triangular form - _Emeric Deutsch_, Jan 17 2007
%t A126988 Table[If[Mod[n, m]==0, n/m, 0], {n,1,12}, {m,1,n}]//Flatten (* _Roger L. Bagula_, Sep 06 2008, simplified by _Franklin T. Adams-Watters_, Aug 24 2011 *)
%o A126988 (Haskell)
%o A126988 a126988 n k = a126988_tabl !! (n-1) !! (k-1)
%o A126988 a126988_row n = a126988_tabl !! (n-1)
%o A126988 a126988_tabl = zipWith (zipWith (*)) a010766_tabl a051731_tabl
%o A126988 -- _Reinhard Zumkeller_, Jan 20 2014
%o A126988 (PARI) {T(n,k) = if(n%k==0, n/k, 0)}; \\ _G. C. Greubel_, May 29 2019
%o A126988 (Magma) [[(n mod k) eq 0 select n/k else 0: k in [1..n]]: n in [1..12]]; // _G. C. Greubel_, May 29 2019
%o A126988 (Sage)
%o A126988 def T(n, k):
%o A126988 if (n%k==0): return n/k
%o A126988 else: return 0
%o A126988 [[T(n, k) for k in (1..n)] for n in (1..12)] # _G. C. Greubel_, May 29 2019
%Y A126988 Cf. A000203, A008284, A127446, A244051, A328361.
%K A126988 nonn,easy,tabl
%O A126988 1,2
%A A126988 _Gary W. Adamson_, Dec 31 2006
%E A126988 Edited by _N. J. A. Sloane_, Jan 24 2007
%E A126988 Comment from _Emeric Deutsch_ made name by _Franklin T. Adams-Watters_, Aug 24 2011