A143235 - OEIS

%I #13 Sep 12 2024 11:46:21

%S 1,2,4,2,4,4,3,6,6,9,2,4,4,6,4,4,8,8,12,8,16,2,4,4,6,4,8,4,4,8,8,12,8,

%T 16,8,16,3,6,6,9,6,12,6,12,9,4,8,8,12,8,16,8,16,12,16,2,4,4,6,4,8,4,8,

%U 6,8,4,6,12,12,18,12,24,12,24,18,24,12,36,2,4,4,6,4,8,4,8,6,8,4,12,4

%N Triangle read by rows: T(n,k) = tau(n)*tau(k), the product of the number of divisors.

%C The triangle can also be created by the triple matrix product A130209 * A000012 * A130209.

%H G. C. Greubel, <a href="/A143235/b143235.txt">Rows n = 1..50 of the triangle, flattened</a>

%F T(n,k) = A000005(n)*A000005(k), for 1 <= k <= n, n >= 1.

%F Sum_{k=1..n} T(n, k) = A143236(n) (row sums).

%e First few rows of the triangle =

%e   1;

%e   2, 4;

%e   2, 4, 4;

%e   3, 6, 6,  9;

%e   2, 4, 4,  6, 4;

%e   4, 8, 8, 12, 8, 16;

%e   2, 4, 4,  6, 4,  8, 4;

%e   4, 8, 8, 12, 8, 16, 8, 16;

%e   3, 6, 6,  9, 6, 12, 6, 12, 9;

%e   ...

%e T(9,6) = 12 = d(9)*d(6) = 3*4.

%t A143235[n_, k_]:= DivisorSigma[0, n]*DivisorSigma[0, k];

%t Table[A143235[n, k], {n,15}, {k,n}]//Flatten (* _G. C. Greubel_, Sep 12 2024 *)

%o (Magma)

%o A143235:= func< n,k | NumberOfDivisors(n)*NumberOfDivisors(k) >;

%o [A143235(n,k): k in [1..n], n in [1..14]]; // _G. C. Greubel_, Sep 12 2024

%o (SageMath)

%o def A143235(n,k): return sigma(n,0)*sigma(k,0)

%o flatten([[A143235(n,k) for k in range(1,n+1)] for n in range(1,15)]) # _G. C. Greubel_, Sep 12 2024

%Y Cf. A000005, A035116 (right diagonal), A143236 (row sums).

%K nonn,tabl,easy

%O 1,2

%A _Gary W. Adamson_, Aug 01 2008