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

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, 48, 96, 64, 15, 45, 60, 105, 90, 180, 120, 225, 13, 39, 52, 91, 78, 156, 104, 195, 169, 18, 54, 72, 126, 108, 216, 144, 270, 234, 324, 12, 36, 48, 84, 72, 144, 96, 180, 156, 216, 144

Offset: 1

Author

Gary W. Adamson, Aug 01 2008

Keywords

• nonn
• tabl

Examples

			First few rows of the triangle =
   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, 48,  96,  64;
  15, 45, 60, 105, 90, 180, 120, 225;
  13, 39, 52,  91, 78, 156, 104, 195, 169;
  ...
T(6,3) = 48 = sigma(6)*sigma(3) = 12*4
		

Links

• G. C. Greubel, Rows n = 1..50 of the triangle, flattened

Crossrefs

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

Programs

Magma

A143237:= func< n,k | DivisorSigma(1,n)*DivisorSigma(1,k) >;
[A143237(n,k): k in [1..n], n in [1..15]]; // G. C. Greubel, Sep 12 2024

Mathematica

A143237[n_, k_]:= DivisorSigma[1,n]*DivisorSigma[1,k];
Table[A143237[n,k], {n,15}, {k,n}]//Flatten (* G. C. Greubel, Sep 12 2024 *)

SageMath

def A143237(n,k): return sigma(n,1)*sigma(k,1)
flatten([[A143237(n,k) for k in range(1,n+1)] for n in range(1,16)]) # G. C. Greubel, Sep 12 2024

Formula

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

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

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

Extensions

New title by G. C. Greubel, Sep 12 2024