Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #11 Jun 20 2019 04:19:20
%S 0,0,0,0,0,0,0,0,1,1,1,0,0,1,1,0,1,2,3,1,2,2,3,1,3,3,3,1,2,3,3,1,3,3,
%T 4,0,4,5,5,2,5,6,5,2,4,6,6,2,5,7,8,2,5,6,9,4,7,7,9,4,7,8,8,4,8,9,9,3,
%U 8,8,10,1,9,9,10,3,8,10,9,4,8,11,11,3,9
%N Number of partitions of n into two parts with smaller part nonsquarefree and larger part squarefree.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{i=1..floor(n/2)} (1 - mu(i)^2) * mu(n-i)^2, where mu is the Möbius function (A008683).
%t Table[Sum[(1 - MoebiusMu[k]^2) (MoebiusMu[n - k]^2), {k, Floor[n/2]}], {n, 80}]
%Y Cf. A008683, A008966, A294232.
%K nonn,easy
%O 1,18
%A _Wesley Ivan Hurt_, Oct 25 2017