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A110662
Triangle read by rows: T(n,k) is the sum of the sums of divisors of k, k+1, ..., n (1 <= k <= n).
2
1, 4, 3, 8, 7, 4, 15, 14, 11, 7, 21, 20, 17, 13, 6, 33, 32, 29, 25, 18, 12, 41, 40, 37, 33, 26, 20, 8, 56, 55, 52, 48, 41, 35, 23, 15, 69, 68, 65, 61, 54, 48, 36, 28, 13, 87, 86, 83, 79, 72, 66, 54, 46, 31, 18, 99, 98, 95, 91, 84, 78, 66, 58, 43, 30, 12, 127, 126, 123, 119, 112
OFFSET
1,2
COMMENTS
Equals A000012 * (A000203 * 0^(n-k)) * A000012, 1 <= k <= n. - Gary W. Adamson, Jul 26 2008
Row sums = A143128. - Gary W. Adamson, Jul 26 2008
LINKS
Indranil Ghosh, Rows 1..100, flattened
FORMULA
T(n, k) = Sum_{j=k..n} sigma(j), where sigma(j) is the sum of the divisors of j.
T(n, n) = sigma(n) = A000203(n) = sum of divisors of n.
T(n, 1) = Sum_{j=1..n} sigma(j) = A024916(n).
EXAMPLE
T(4,2)=14 because the divisors of 2 are {1,2}, the divisors of 3 are {1,3} and the divisors of 4 are {1,2,4}; sum of all these divisors is 14.
Triangle begins:
1;
4, 3;
8, 7, 4;
15, 14, 11, 7;
21, 20, 17, 13, 6;
...
MAPLE
with(numtheory): T:=(n, k)->add(sigma(j), j=k..n): for n from 1 to 12 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form
MATHEMATICA
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 *)
CROSSREFS
Cf. A143128.
Sequence in context: A117956 A241638 A360689 * A265289 A302258 A132021
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch, Aug 02 2005
STATUS
approved