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A143237 Triangle read by rows, T(n, k) = A000203(n)*A000203(k), for n >= 1, 1 <= k <= n.

%I A143237 #10 Sep 12 2024 11:28:47
%S A143237 1,3,9,4,12,16,7,21,28,49,6,18,24,42,36,12,36,48,84,72,144,8,24,32,56,
%T A143237 48,96,64,15,45,60,105,90,180,120,225,13,39,52,91,78,156,104,195,169,
%U A143237 18,54,72,126,108,216,144,270,234,324,12,36,48,84,72,144,96,180,156,216,144
%N A143237 Triangle read by rows, T(n, k) = A000203(n)*A000203(k), for n >= 1, 1 <= k <= n.
%H A143237 G. C. Greubel, <a href="/A143237/b143237.txt">Rows n = 1..50 of the triangle, flattened</a>
%F A143237 Triangle read by rows, A130208 * A000012 * A130208, for 1 <= k <= n, n >= 1.
%F A143237 T(n, k) = sigma(n)*sigma(k), where sigma(n) = A000203(n).
%F A143237 Sum_{k=1..n} T(n, k) = A143238(n) (row sums).
%e A143237 First few rows of the triangle =
%e A143237    1;
%e A143237    3,  9;
%e A143237    4, 12, 16;
%e A143237    7, 21, 28,  49;
%e A143237    6, 18, 24,  42, 36;
%e A143237   12, 36, 48,  84, 72, 144;
%e A143237    8, 24, 32,  56, 48,  96,  64;
%e A143237   15, 45, 60, 105, 90, 180, 120, 225;
%e A143237   13, 39, 52,  91, 78, 156, 104, 195, 169;
%e A143237   ...
%e A143237 T(6,3) = 48 = sigma(6)*sigma(3) = 12*4
%t A143237 A143237[n_, k_]:= DivisorSigma[1,n]*DivisorSigma[1,k];
%t A143237 Table[A143237[n,k], {n,15}, {k,n}]//Flatten (* _G. C. Greubel_, Sep 12 2024 *)
%o A143237 (Magma)
%o A143237 A143237:= func< n,k | DivisorSigma(1,n)*DivisorSigma(1,k) >;
%o A143237 [A143237(n,k): k in [1..n], n in [1..15]]; // _G. C. Greubel_, Sep 12 2024
%o A143237 (SageMath)
%o A143237 def A143237(n,k): return sigma(n,1)*sigma(k,1)
%o A143237 flatten([[A143237(n,k) for k in range(1,n+1)] for n in range(1,16)]) # _G. C. Greubel_, Sep 12 2024
%Y A143237 Cf. A000203, A024916, A072861 (right diagonal), A130208, A143238 (row sums).
%K A143237 nonn,tabl
%O A143237 1,2
%A A143237 _Gary W. Adamson_, Aug 01 2008
%E A143237 New title by _G. C. Greubel_, Sep 12 2024