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Triangle read by rows, T(n, k) = A000203(n)*A000203(k), for n >= 1, 1 <= k <= n.
2

%I #10 Sep 12 2024 11:28:47

%S 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 48,96,64,15,45,60,105,90,180,120,225,13,39,52,91,78,156,104,195,169,

%U 18,54,72,126,108,216,144,270,234,324,12,36,48,84,72,144,96,180,156,216,144

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

%H G. C. Greubel, <a href="/A143237/b143237.txt">Rows n = 1..50 of the triangle, flattened</a>

%F Triangle read by rows, A130208 * A000012 * A130208, for 1 <= k <= n, n >= 1.

%F T(n, k) = sigma(n)*sigma(k), where sigma(n) = A000203(n).

%F Sum_{k=1..n} T(n, k) = A143238(n) (row sums).

%e First few rows of the triangle =

%e 1;

%e 3, 9;

%e 4, 12, 16;

%e 7, 21, 28, 49;

%e 6, 18, 24, 42, 36;

%e 12, 36, 48, 84, 72, 144;

%e 8, 24, 32, 56, 48, 96, 64;

%e 15, 45, 60, 105, 90, 180, 120, 225;

%e 13, 39, 52, 91, 78, 156, 104, 195, 169;

%e ...

%e T(6,3) = 48 = sigma(6)*sigma(3) = 12*4

%t A143237[n_, k_]:= DivisorSigma[1,n]*DivisorSigma[1,k];

%t Table[A143237[n,k], {n,15}, {k,n}]//Flatten (* _G. C. Greubel_, Sep 12 2024 *)

%o (Magma)

%o A143237:= func< n,k | DivisorSigma(1,n)*DivisorSigma(1,k) >;

%o [A143237(n,k): k in [1..n], n in [1..15]]; // _G. C. Greubel_, Sep 12 2024

%o (SageMath)

%o def A143237(n,k): return sigma(n,1)*sigma(k,1)

%o flatten([[A143237(n,k) for k in range(1,n+1)] for n in range(1,16)]) # _G. C. Greubel_, Sep 12 2024

%Y Cf. A000203, A024916, A072861 (right diagonal), A130208, A143238 (row sums).

%K nonn,tabl

%O 1,2

%A _Gary W. Adamson_, Aug 01 2008

%E New title by _G. C. Greubel_, Sep 12 2024