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Sum of the differences of the larger and smaller parts in the partitions of 2n into two squarefree parts or two nonsquarefree parts.
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%I #11 Feb 10 2018 21:58:12

%S 0,2,4,12,4,24,20,54,40,72,70,114,62,116,62,182,126,292,134,330,182,

%T 412,190,460,202,468,380,518,490,632,462,692,458,890,562,1184,638,

%U 1088,590,1206,590,1430,678,1556,986,1578,952,1772,1032,1876,1214,1986,1326

%N Sum of the differences of the larger and smaller parts in the partitions of 2n into two squarefree parts or two nonsquarefree parts.

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

%F a(n) = 2 * Sum_{i=1..n} (n - i) * [A008966(i) = A008966(2n-i)], where [] is the Iverson bracket.

%t Table[2 Sum[(n - k) KroneckerDelta[MoebiusMu[k]^2, MoebiusMu[2 n - k]^2], {k, n}], {n, 80}]

%Y Cf. A008966, A294097.

%K nonn,easy

%O 1,2

%A _Wesley Ivan Hurt_, Oct 22 2017