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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
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. A143127.
Sequence in context: A371905 A371908 A143956 * A143124 A205400 A205850
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.)