%I
%S 0,0,1,1,1,2,1,3,3,4,2,7,4,9,7,9,7,15,9,18,14,19,12,27,15,26,21,30,21,
%T 44,25,43,35,46,34,58,34,59,46,64,43,82,47,80,64,83,58,107,65,106,79,
%U 110,75,137,86,128,98,132,92,172,96,155,122,161,118,198,119,188,147
%N Number of partitions of n into 3 parts such that the 'middle' part is relatively prime to each of the other two parts.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((nk)/2)} floor(1/gcd(i,k)) * floor(1/gcd(i,nik)).
%t Table[Sum[Sum[Floor[1/GCD[i, k]]*Floor[1/GCD[i, n  i  k]], {i, k, Floor[(n  k)/2]}], {k, Floor[n/3]}], {n, 80}]
%Y Cf. A340283, A340285.
%K nonn
%O 1,6
%A _Wesley Ivan Hurt_, Jan 02 2021
