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Numerator of sum of all elements M(i,j,k) = i*j/k, (i,j,k = 1..n). a(n) = Numerator[Sum[Sum[Sum[i*j/k,{i,1,n}],{j,1,n}],{k,1,n}]].
1

%I #4 Mar 31 2012 13:20:25

%S 1,27,66,625,2055,21609,10164,123282,320805,4465505,920821,14537549,

%T 104285363,41010655,47830280,2816662204,6447760119,139131611847,

%U 26153100905,29313445875,13068630729,111103313343,91973556693

%N Numerator of sum of all elements M(i,j,k) = i*j/k, (i,j,k = 1..n). a(n) = Numerator[Sum[Sum[Sum[i*j/k,{i,1,n}],{j,1,n}],{k,1,n}]].

%F a(n) = Numerator[Sum[Sum[Sum[i*j/k, {i, 1, n}], {j, 1, n}], {k, 1, n}]]

%e Sum[M(i,j,k)] begins 1, 27/32, 66, 625/3, 2055/4, 21609/20, ... So a(4) = 625.

%t Table[ Numerator[ Sum[ i*j/k, {i, n}, {j, n}, {k, n}]], {n, 23}]

%Y Corresponding denominator of Sum[M(i, j, k)] is A099866

%Y Cf. A099866.

%K nonn,frac

%O 1,2

%A _Alexander Adamchuk_, Oct 28 2004