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%I #4 Apr 05 2021 03:53:04
%S 0,0,1,1,2,2,4,4,6,6,10,8,14,12,16,16,24,18,30,24,32,30,44,32,50,42,
%T 54,48,70,48,79,64,80,72,96,72,113,90,112,96,138,96,153,120,144,132,
%U 182,128,195,150,192,168,232,162,239,192,240,210,287,192,305,240,288,256
%N Number of partitions of n into 3 parts, at least 2 of which are coprime.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} sign(floor(1/gcd(i, j)) + floor(1/gcd(i, n-i-j)) + floor(1/gcd(j, n-i-j))).
%e a(12) = 8; [10,1,1], [9,2,1], [8,3,1], [7,4,1], [7,3,2], [6,5,1], [5,5,2], [5,4,3].
%t Table[Sum[Sum[Sign[Floor[1/GCD[i, j]] + Floor[1/GCD[i, n - i - j]] + Floor[1/GCD[j, n - i - j]]], {i, j, Floor[(n - j)/2]}], {j, Floor[n/3]}], {n, 100}]
%Y Cf. A023023, A069905.
%K nonn
%O 1,5
%A _Wesley Ivan Hurt_, Apr 05 2021
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