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URL: https://oeis.org/A143235

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A143235
Triangle read by rows: T(n,k) = tau(n)*tau(k), the product of the number of divisors.
3
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, 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, 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
OFFSET
1,2
COMMENTS
The triangle can also be created by the triple matrix product A130209 * A000012 * A130209.
FORMULA
T(n,k) = A000005(n)*A000005(k), for 1 <= k <= n, n >= 1.
Sum_{k=1..n} T(n, k) = A143236(n) (row sums).
EXAMPLE
First few rows of the triangle =
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, 16, 8, 16;
3, 6, 6, 9, 6, 12, 6, 12, 9;
...
T(9,6) = 12 = d(9)*d(6) = 3*4.
MATHEMATICA
A143235[n_, k_]:= DivisorSigma[0, n]*DivisorSigma[0, k];
Table[A143235[n, k], {n, 15}, {k, n}]//Flatten (* G. C. Greubel, Sep 12 2024 *)
PROG
(Magma)
A143235:= func< n, k | NumberOfDivisors(n)*NumberOfDivisors(k) >;
[A143235(n, k): k in [1..n], n in [1..14]]; // G. C. Greubel, Sep 12 2024
(SageMath)
def A143235(n, k): return sigma(n, 0)*sigma(k, 0)
flatten([[A143235(n, k) for k in range(1, n+1)] for n in range(1, 15)]) # G. C. Greubel, Sep 12 2024
CROSSREFS
Cf. A000005, A035116 (right diagonal), A143236 (row sums).
Sequence in context: A004020 A363290 A246436 * A069465 A047947 A018838
KEYWORD
nonn,tabl,easy
AUTHOR
Gary W. Adamson, Aug 01 2008
STATUS
approved