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%I #5 Jan 03 2021 15:54:36
%S 0,0,1,1,2,2,4,4,6,6,10,8,14,12,16,16,22,18,28,24,32,30,42,32,48,42,
%T 52,48,64,48,74,64,78,72,90,72,104,88,108,96,126,96,140,118,142,130,
%U 166,128,180,150,186,164,212,162,222,190,230,206,260,192,280,236,280,252
%N Number of partitions of n into 3 parts such that the 'middle' part is relatively prime to at least one other part.
%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((n-k)/2)} sign(floor(1/gcd(i,k)) + floor(1/gcd(i,n-i-k))).
%t Table[Sum[Sum[Sign[Floor[1/GCD[k, i]] + Floor[1/GCD[i, n - i - k]]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 80}]
%Y Cf. A340279, A340282.
%K nonn
%O 1,5
%A _Wesley Ivan Hurt_, Jan 02 2021
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