|
%I #5 Aug 03 2019 21:47:30
%S 0,0,0,0,0,0,6,6,12,17,29,40,62,77,109,139,186,229,299,361,454,547,
%T 672,797,967,1132,1352,1574,1850,2131,2486,2841,3276,3723,4256,4805,
%U 5461,6125,6910,7721,8655,9621,10739,11883,13193,14550,16083,17669,19460
%N Number of squarefree parts in the partitions of n into 6 parts.
%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)} (mu(i)^2 + mu(j)^2 + mu(k)^2 + mu(l)^2 + mu(m)^2 + mu(n-i-j-k-l-m)^2), where mu is the Möbius function (A008683).
%t Table[Sum[Sum[Sum[Sum[Sum[MoebiusMu[i]^2 + MoebiusMu[j]^2 + MoebiusMu[k]^2 + MoebiusMu[l]^2 + MoebiusMu[m]^2 + 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.
%K nonn
%O 0,7
%A _Wesley Ivan Hurt_, Aug 03 2019
|
