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%I A308953 #10 Mar 03 2024 07:49:35
%S A308953 0,0,0,0,0,0,0,7,8,18,20,44,60,104,126,180,224,340,396,551,640,882,
%T A308953 1034,1357,1536,2025,2314,2943,3304,4176,4680,5797,6464,7887,8806,
%U A308953 10605,11664,14023,15504,18291,20040,23657,25956,30272,32956,38295,41860,48269
%N A308953 Sum of all the parts in the partitions of n into 7 squarefree parts.
%H A308953 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308953 a(n) = n * Sum_{o=1..floor(n/7)} Sum_{m=o..floor((n-o)/6)} Sum_{l=m..floor((n-m-o)/5)} Sum_{k=l..floor((n-l-m-o)/4)} Sum_{j=k..floor((n-k-l-m-o)/3} Sum_{i=j..floor((n-j-k-l-m-o)/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)^2, where mu is the Möbius function (A008683).
%F A308953 a(n) = n * A308952(n).
%F A308953 a(n) = A308954(n) + A308955(n) + A308956(n) + A308957(n) + A308958(n) + A308959(n) + A308960(n).
%t A308953 Table[Total[Flatten[Select[IntegerPartitions[n,{7}],AllTrue[#,SquareFreeQ]&]]],{n,0,50}] (* _Harvey P. Dale_, Feb 25 2024 *)
%Y A308953 Cf. A008683, A308952, A308954, A308955, A308956, A308957, A308958, A308959, A308960.
%K A308953 nonn
%O A308953 0,8
%A A308953 _Wesley Ivan Hurt_, Jul 03 2019

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