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%I #15 Jan 18 2021 09:56:56
%S 1,1,2,3,4,6,8,11,12,18,20,26,29,39,39,54,54,69,73,94,89,119,118,144,
%T 145,185,169,225,215,259,258,317,291,378,357,423,410,511,457,588,547,
%U 639,626,764,679,861,792,933,896,1089,963,1203,1112,1296,1240,1495,1302,1650
%N Number of partitions of n into 4 unordered relatively prime parts.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F G.f.: Sum_{k>=1} mu(k)*x^(4*k) / Product_{j=1..4} (1 - x^(j*k)). - _Ilya Gutkovskiy_, Aug 31 2019
%F a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} [gcd(k,j,i,n-i-j-k) = 1], where [ ] is the Iverson bracket. - _Wesley Ivan Hurt_, Jan 17 2021
%t Table[Sum[Sum[Sum[KroneckerDelta[GCD[k, j, i, (n - i - j - k)], 1], {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 4, 80}] (* _Wesley Ivan Hurt_, Jan 17 2021 *)
%Y Column 4 of A282750.
%K nonn
%O 4,3
%A _David W. Wilson_
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