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Number of partitions of n into 3 parts such that the largest part is relatively prime to each of the other two parts.

2

`%I #4 Jan 03 2021 15:55:02
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`%S 0,0,1,1,1,2,2,3,3,5,5,7,6,9,8,11,10,16,12,18,15,20,19,28,21,30,25,34,
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`%T 27,44,30,44,36,50,39,60,43,62,51,69,52,85,56,83,68,86,68,109,71,109,
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`%U 84,110,84,138,91,132,105,138,104,176,111,162,131,171,127,204,129,193
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`%N Number of partitions of n into 3 parts such that the largest part is relatively prime to each of the other two parts.
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`%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
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`%F a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} floor(1/gcd(n-i-k,k)) * floor(1/gcd(n-i-k,i)).
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`%t Table[Sum[Sum[Floor[1/GCD[n - i - k, k]]*Floor[1/GCD[n - i - k, i]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 80}]
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`%Y Cf. A340283, A340284.
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`%K nonn
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`%O 1,6
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`%A _Wesley Ivan Hurt_, Jan 02 2021
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