

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
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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^(nk)) * 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



