A099866 - OEIS

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A099866

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

1, 2, 1, 3, 4, 20, 5, 35, 56, 504, 70, 770, 3960, 1144, 1001, 45045, 80080, 1361360, 204204, 184756, 67184, 470288, 323323, 7436429, 27457584, 228813200, 106234700, 2868336900, 356948592, 10351509168, 145568097675, 45581929575, 85801279200

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..33.

FORMULA

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

a(n) = denominator of ((n^2+n)/2)^2*Sum(1/i, i=1..n). - Vladeta Jovovic, Oct 30 2004

EXAMPLE

Sum[M(i,j,k)] begins 1, 27/2, 66, 625/3, 2055/4, 21609/20, ... So a(2) = 2.

MATHEMATICA

Table[ Denominator[ Sum[ i*j/k, {i, n}, {j, n}, {k, n}]], {n, 33}]