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 A110661 Triangle read by rows: T(n,k) = total number of divisors of k, k+1, ..., n (1 <= k <= n). 2
 1, 3, 2, 5, 4, 2, 8, 7, 5, 3, 10, 9, 7, 5, 2, 14, 13, 11, 9, 6, 4, 16, 15, 13, 11, 8, 6, 2, 20, 19, 17, 15, 12, 10, 6, 4, 23, 22, 20, 18, 15, 13, 9, 7, 3, 27, 26, 24, 22, 19, 17, 13, 11, 7, 4, 29, 28, 26, 24, 21, 19, 15, 13, 9, 6, 2, 35, 34, 32, 30, 27, 25, 21, 19, 15, 12, 8, 6, 37, 36, 34 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Equals A000012 * (A000005 * 0^(n-k)) * A000012, 1 <= k <= n. - Gary W. Adamson, Jul 26 2008 Row sums = A143127. - Gary W. Adamson, Jul 26 2008 LINKS G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened FORMULA T(n, k) = Sum_{j=k..n} tau(j), where tau(j) is the number of divisors of j, and 1 <= k <= n. T(n,n) = tau(n) = A000005(n) = number of divisors of n. T(n,1) = Sum_{j=1..n} tau(j) = A006218(n). EXAMPLE T(4,2)=7 because 2 has 2 divisors, 3 has 2 divisors and 4 has 3 divisors. Triangle begins: 1; 3, 2; 5, 4, 2; 8, 7, 5, 3; 10, 9, 7, 5, 2; ... MAPLE with(numtheory): T:=(n, k)->add(tau(j), j=k..n): for n from 1 to 13 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form MATHEMATICA T[n_, n_] := DivisorSigma[0, n]; T[n_, k_] := Sum[DivisorSigma[0, j], {j, k, n}]; Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* G. C. Greubel, Sep 03 2017 *) CROSSREFS Cf. A000005, A006218. Cf. A143127. Sequence in context: A371905 A371908 A143956 * A143124 A205400 A205850 Adjacent sequences: A110658 A110659 A110660 * A110662 A110663 A110664 KEYWORD nonn,tabl AUTHOR Emeric Deutsch, Aug 02 2005 STATUS approved

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Last modified April 21 03:11 EDT 2024. Contains 371850 sequences. (Running on oeis4.)