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%I #14 Jun 20 2021 11:10:47
%S 0,0,0,0,0,0,0,4,5,6,7,8,9,10,11,20,22,33,36,39,42,45,48,63,67,71,75,
%T 79,83,87,91,111,116,121,126,149,155,161,167,193,200,207,214,221,228,
%U 235,242,273,281,314,323,332,341,377,387,425,436,447,458,469
%N Sum of the larger parts of the partitions of n into two parts with smaller part nonsquarefree.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{i=1..floor(n/2)} (n - i) * (1 - mu(i)^2), where mu is the Möbius function (A008683).
%t Table[Sum[(n - k) (1 - MoebiusMu[k]^2), {k, Floor[n/2]}], {n, 80}]
%t Table[Total[Select[IntegerPartitions[n,{2}],!SquareFreeQ[#[[2]]]&][[All,1]]],{n,60}] (* _Harvey P. Dale_, Jun 20 2021 *)
%Y Cf. A008683, A008966, A294236.
%K nonn,easy
%O 1,8
%A _Wesley Ivan Hurt_, Oct 25 2017