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%I A110662 #24 Feb 07 2022 03:45:34
%S A110662 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,
%T A110662 26,20,8,56,55,52,48,41,35,23,15,69,68,65,61,54,48,36,28,13,87,86,83,
%U A110662 79,72,66,54,46,31,18,99,98,95,91,84,78,66,58,43,30,12,127,126,123,119,112
%N A110662 Triangle read by rows: T(n,k) is the sum of the sums of divisors of k, k+1, ..., n (1 <= k <= n).
%C A110662 Equals A000012 * (A000203 * 0^(n-k)) * A000012, 1 <= k <= n. - _Gary W. Adamson_, Jul 26 2008
%C A110662 Row sums = A143128. - _Gary W. Adamson_, Jul 26 2008
%H A110662 Indranil Ghosh, <a href="/A110662/b110662.txt">Rows 1..100, flattened</a>
%F A110662 T(n, k) = Sum_{j=k..n} sigma(j), where sigma(j) is the sum of the divisors of j.
%F A110662 T(n, n) = sigma(n) = A000203(n) = sum of divisors of n.
%F A110662 T(n, 1) = Sum_{j=1..n} sigma(j) = A024916(n).
%e A110662 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.
%e A110662 Triangle begins:
%e A110662    1;
%e A110662    4,  3;
%e A110662    8,  7,  4;
%e A110662   15, 14, 11,  7;
%e A110662   21, 20, 17, 13,  6;
%e A110662   ...
%p A110662 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
%t A110662 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 *)
%Y A110662 Cf. A000203, A024916.
%Y A110662 Cf. A143128.
%K A110662 nonn,tabl
%O A110662 1,2
%A A110662 _Emeric Deutsch_, Aug 02 2005

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