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%I #16 Feb 05 2018 02:59:16
%S 0,1,1,2,1,2,2,4,2,2,2,5,4,3,3,7,5,5,3,8,5,6,4,10,6,6,6,10,7,6,6,12,8,
%T 9,7,17,9,8,8,16,10,9,11,18,13,9,9,19,13,10,8,21,14,14,8,20,14,15,11,
%U 22,15,14,14,23,15,14,14,27,16,17,13,33,17,18,16
%N Number of partitions of n into two squarefree parts or two nonsquarefree positive integer parts.
%C Number of distinct rectangles with both length and width squarefree or both nonsquarefree positive integers such that L + W = n, W <= L. For example, a(12) = 5; the rectangles are 1 X 11, 2 X 10, 4 X 8, 5 X 7, 6 X 6. - _Wesley Ivan Hurt_, Nov 04 2017
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{i=1..floor(n/2)} [A008966(i) = A008966(n-i)], where [] is the Iverson bracket.
%t Table[Sum[KroneckerDelta[MoebiusMu[k]^2, MoebiusMu[n - k]^2], {k, Floor[n/2]}], {n, 80}]
%o (PARI) a(n) = sum(i=1, n\2, issquarefree(i) == issquarefree(n-i)); \\ _Michel Marcus_, Nov 08 2017
%Y Cf. A008966, A294101.
%K nonn,easy
%O 1,4
%A _Wesley Ivan Hurt_, Oct 22 2017