|
%I #9 Jan 07 2022 11:09:47
%S 0,0,0,0,0,0,6,7,16,23,46,69,116,150,227,309,442,565,787,998,1326,
%T 1665,2153,2655,3386,4103,5122,6184,7563,8995,10888,12853,15323,17931,
%U 21167,24584,28796,33153,38484,44133,50813,57870,66293,75125,85487,96437,109177
%N Sum of the squarefree parts of the partitions of n into 6 parts.
%H David A. Corneth, <a href="/A309481/b309481.txt">Table of n, a(n) for n = 0..9999</a>
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{m=1..floor(n/6)} Sum_{l=m..floor((n-m)/5)} Sum_{k=l..floor((n-l-m)/4)} Sum_{j=k..floor((n-k-l-m)/3)} Sum_(i=j..floor((n-j-k-l-m)/2)} (i * mu(i)^2 + j * mu(j)^2 + k * mu(k)^2 + l * mu(l)^2 + m * mu(m)^2 + (n-i-j-k-l-m) * mu(n-i-j-k-l-m)^2), where mu is the Möbius function (A008683).
%t Table[Sum[Sum[Sum[Sum[Sum[i * MoebiusMu[i]^2 + j * MoebiusMu[j]^2 + k * MoebiusMu[k]^2 + l * MoebiusMu[l]^2 + m * MoebiusMu[m]^2 + (n - i - j - k - l - m) * MoebiusMu[n - i - j - k - l - m]^2, {i, j, Floor[(n - j - k - l - m)/2]}], {j, k, Floor[(n - k - l - m)/3]}], {k, l, Floor[(n - l - m)/4]}], {l, m, Floor[(n - m)/5]}], {m, Floor[n/6]}], {n, 0, 50}]
%Y Cf. A008683, A309458, A309478, A309479, A309480, A309481, A309482, A309484, A309485, A309486.
%K nonn
%O 0,7
%A _Wesley Ivan Hurt_, Aug 04 2019
|
