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A110662 Triangle read by rows: T(n,k) = 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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

T(n,n)=sigma(n)=A000203(n) =sum of divisors of 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

LINKS

Indranil Ghosh, Rows 1..100, flattened

FORMULA

T(n, k)=sum(sigma(j), j=k..n), where sigma(j) is the sum of the divisors of j.

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. A000203, A024916.

Cf. A143128.

Sequence in context: A200089 A117956 A241638 * A265289 A302258 A132021

Adjacent sequences:  A110659 A110660 A110661 * A110663 A110664 A110665

KEYWORD

nonn,tabl

AUTHOR

Emeric Deutsch, Aug 02 2005

STATUS

approved

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Last modified March 25 08:15 EDT 2019. Contains 321469 sequences. (Running on oeis4.)