A099865 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, 27, 66, 625, 2055, 21609, 10164, 123282, 320805, 4465505, 920821, 14537549, 104285363, 41010655, 47830280, 2816662204, 6447760119, 139131611847, 26153100905, 29313445875, 13068630729, 111103313343, 91973556693

Offset

1,2

Links

Table of n, a(n) for n=1..23.

Formula

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

Example

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

Mathematica

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

Crossrefs

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

Cf. A099866.

Sequence in context: A106200 A303972 A361147 * A065008 A250134 A116353

Adjacent sequences: A099862 A099863 A099864 * A099866 A099867 A099868

Keyword

nonn,frac

Author

Alexander Adamchuk, Oct 28 2004

Status

approved