A326633 - OEIS

%I #14 Sep 29 2021 18:43:32

%S 0,0,0,0,0,0,0,0,0,0,1,1,2,2,4,6,10,12,18,24,36,42,58,71,97,114,149,

%T 176,230,266,338,394,498,575,714,832,1028,1183,1439,1656,2011,2290,

%U 2735,3115,3711,4195,4936,5574,6533,7335,8523,9549,11060,12334,14162

%N Sum of the fifth largest parts of the partitions of n into 10 squarefree parts.

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F a(n) = Sum_{r=1..floor(n/10)} Sum_{q=r..floor((n-r)/9)} Sum_{p=q..floor((n-q-r)/8)} Sum_{o=p..floor((n-p-q-r)/7)} Sum_{m=o..floor((n-o-p-q-r)/6)} Sum_{l=m..floor((n-m-o-p-q-r)/5)} Sum_{k=l..floor((n-l-m-o-p-q-r)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q-r)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q-r)/2)} mu(r)^2 * mu(q)^2 * mu(p)^2 * mu(o)^2 * mu(m)^2 * mu(l)^2 * mu(k)^2 * mu(j)^2 * mu(i)^2 * mu(n-i-j-k-l-m-o-p-q-r)^2 * l, where mu is the Möbius function (A008683).

%F a(n) = A326627(n) - A326628(n) - A326629(n) - A326630(n) - A326631(n) - A326632(n) - A326634(n) - A326635(n) - A326636(n) - A326637(n).

%t Table[Total[Select[IntegerPartitions[n,{10}],AllTrue[#,SquareFreeQ]&][[All,5]]],{n,0,60}] (* _Harvey P. Dale_, Sep 29 2021 *)

%Y Cf. A008683, A326626, A326627, A326628, A326629, A326630, A326631, A326632, A326634, A326635, A326636, A326637.

%K nonn

%O 0,13

%A _Wesley Ivan Hurt_, Jul 14 2019