A303051 - OEIS

%I #8 Jun 20 2019 04:26:51

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

%T 6,0,7,6,7,0,8,7,9,0,0,7,8,0,0,0,7,0,10,0,7,0,10,10,9,0,11,10,0,0,11,

%U 10,11,0,12,12,11,0,13,13,0,0,14,12,14,0,0

%N Number of partitions of n into two distinct parts (p,q) such that p, q and p+q are all squarefree.

%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(n)^2 * mu(i)^2 * mu(n-i)^2, where mu is the Möbius function (A008683).

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

%o (PARI) a(n) = sum(i=1, (n-1)\2, moebius(n)^2*moebius(i)^2*moebius(n-i)^2); \\ _Michel Marcus_, Apr 17 2018

%Y Cf. A008683, A302986.

%K nonn,easy

%O 1,7

%A _Wesley Ivan Hurt_, Apr 17 2018