A303165 - OEIS

%I #10 Sep 17 2020 16:38:17

%S 0,0,1,2,4,2,9,8,16,8,16,18,27,18,40,32,55,32,72,32,91,32,112,54,135,

%T 54,135,80,135,80,164,110,195,110,228,144,263,144,300,182,339,182,380,

%U 224,423,224,423,270,470,270,470,270,521,270,574,270,629,270,686

%N Sum of the squarefree differences |q-p| of the parts in the partitions of n into two distinct parts (p,q) where 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)} (n-2*i) * mu(n-2*i)^2, where mu is the Möbius function (A008683).

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

%Y Cf. A008683, A303205.

%K nonn,easy

%O 1,4

%A _Wesley Ivan Hurt_, Apr 19 2018