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Number of partitions of n into 3 parts such that at least two parts share a common factor > 1.

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`%I #4 Jan 03 2021 15:55:09
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`%S 0,0,0,0,1,1,3,2,5,4,8,5,12,8,15,13,20,12,26,17,30,25,37,22,45,33,50,
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`%T 39,60,32,71,50,75,58,86,54,100,71,104,79,122,68,136,95,138,112,159,
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`%U 92,175,119,181,140,203,116,217,157,225,176,251,133,274,195,273,212,300
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`%N Number of partitions of n into 3 parts such that at least two parts share a common factor > 1.
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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)} (1 - [gcd(k,i) * gcd(k,n-i-k) * gcd(i,n-i-k) = 1]), where [ ] is the Iverson bracket.
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`%t Table[Sum[Sum[1 - Floor[1/GCD[k, i]]*Floor[1/GCD[k, n - i - k]]* Floor[1/GCD[i, n - i - k]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 80}]
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`%Y Cf. A307719.
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`%K nonn
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`%O 1,7
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`%A _Wesley Ivan Hurt_, Jan 03 2021
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