A303205 - OEIS

%I #16 Sep 08 2022 08:46:21

%S 0,0,1,1,2,0,3,2,2,0,3,2,4,0,3,4,6,0,5,2,4,0,7,4,6,0,6,4,7,0,8,6,7,0,

%T 6,6,9,0,8,6,12,0,13,8,9,0,12,8,11,0,9,8,13,0,9,6,12,0,15,8,16,0,12,

%U 10,12,0,17,12,13,0,18,10,20,0,14,12,15,0,21

%N Number of rectangles with squarefree area and dimensions p and |q-p| such that n = p + q and p < q.

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

%F a(n) = Sum_{i=1..floor((n-1)/2} mu(i*(n-2*i))^2, where mu is the Möbius function (A008683).

%t Table[Sum[MoebiusMu[i (n - 2 i)]^2, {i, Floor[(n - 1)/2]}], {n, 100}]

%o (Magma) [0, 0] cat [&+[MoebiusMu(k*(n-2*k))^2: k in [1..((n-1) div 2)]]: n in [3..80]]; // _Vincenzo Librandi_, Apr 21 2018

%o (PARI) a(n) = sum(i=1, (n-1)\2, moebius(i*(n-2*i))^2); \\ _Michel Marcus_, Apr 21 2018

%Y Cf. A008683, A303165.

%K nonn,easy

%O 1,5

%A _Wesley Ivan Hurt_, Apr 19 2018