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Number of partitions of n into 4 parts such that the sum of the smallest two parts and the sum of the largest two parts are relatively prime.
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%I #4 Jan 19 2021 21:04:16

%S 0,0,0,0,0,1,0,3,1,4,2,11,1,18,7,14,11,39,10,54,14,40,31,94,26,99,53,

%T 101,49,185,34,225,102,162,123,220,96,378,174,269,160,511,117,588,229,

%U 354,314,764,235,747,318,607,395,1089,340,882,487,849,640,1495,406,1650

%N Number of partitions of n into 4 parts such that the sum of the smallest two parts and the sum of the largest two parts are relatively prime.

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} floor(1/gcd(k+j,n-k-j)).

%t Table[Sum[Sum[Sum[Floor[1/GCD[k + j, n - k - j]], {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 80}]

%K nonn

%O 0,8

%A _Wesley Ivan Hurt_, Jan 19 2021