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

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`%I #5 Jan 03 2021 15:54:48
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`%S 0,0,1,1,2,2,3,4,4,5,6,8,7,10,9,12,11,17,13,20,16,21,18,29,21,31,26,
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`%T 35,27,46,29,46,37,50,39,62,40,63,51,70,50,87,54,85,69,88,65,112,71,
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`%U 111,84,112,81,140,89,134,103,138,99,178,105,164,131,171,126,207,125,195,152
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`%N Number of partitions of n into 3 parts such that the smallest 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(k,i)) * floor(1/gcd(k,n-i-k)).
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`%t Table[Sum[Sum[Floor[1/GCD[k, i]]*Floor[1/GCD[k, n - i - k]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 80}]
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`%Y Cf. A340284, A340285.
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`%K nonn
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`%O 1,5
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`%A _Wesley Ivan Hurt_, Jan 02 2021
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