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T(n,n) = sigma(n) = A000203(n) = sum of divisors of n.
T(n,1) = Sum_{j=1..n} sigma(j) = A024916(n).
Row sums = A143128: (1, 7, 19, 47, 77, ...) - Gary W. Adamson, Jul 26 2008
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Triangle read by rows: T(n,k) = is the sum of the sums of divisors of k, k+1, ..., n (1 <= k <= n).
T(n,n) = sigma(n) = A000203(n) = sum of divisors of n. T(n,1)=sum_{j=1..n} sigma(j) = A024916(n).
T(n,1) = Sum_{j=1..n} sigma(j) = A024916(n).
Equals A000012 * (A000203 * 0^(n-k)) * A000012, 1 <= k <= n. - Gary W. Adamson, Jul 26 2008
Row sums = A143128: (1, 7, 19, 47, 77, ...) - Gary W. Adamson, Jul 26 2008
T(n, k) = Sum_{j=sum(k..n} sigma(j), j=k..n), where sigma(j) is the sum of the divisors of j.
1;
4, 3;
8, 7, 4;
15, 14, 11, 7;
21, 20, 17, 13, 6;
...
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T[n_, n_] := DivisorSigma[1, n]; T[n_, k_] := Sum[DivisorSigma[1, j], {j, k, n}]; Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* G. C. Greubel, Sep 03 2017 *)
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