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%I #20 Dec 11 2023 21:45:53
%S 0,0,1,1,3,2,4,3,5,4,6,5,8,7,10,8,10,7,12,9,13,9,15,11,17,12,17,15,18,
%T 15,20,17,22,16,22,15,23,18,26,20,28,20,29,21,28,23,30,24,32,25,33,26,
%U 34,23,36,27,37,27,39,29,41,29,40,34,42,34,44,36,46
%N Number of partitions of 2n into two parts with at least one nonsquarefree part.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{i=1..n} 1 - mu(2n-i)^2 * mu(i)^2, where mu is the Möbius function (A008683).
%F a(n) = n - A280226(n). - _Wesley Ivan Hurt_, Dec 11 2023
%t Table[Sum[1 - MoebiusMu[2 n - i]^2*MoebiusMu[i]^2, {i, n}], {n, 100}]
%o (Magma) [&+[(1-MoebiusMu(2*n-k)^2*MoebiusMu(k)^2): k in [1..n]]: n in [1..70]]; // _Vincenzo Librandi_, Apr 09 2018
%o (PARI) a(n) = sum(i=1, n, 1 - moebius(2*n-i)^2*moebius(i)^2); \\ _Michel Marcus_, Apr 09 2018
%Y Cf. A008683, A013929, A280226, A294097.
%K nonn
%O 1,5
%A _Wesley Ivan Hurt_, Apr 06 2018