A023024 Number of partitions of n into 4 unordered relatively prime parts.

1, 1, 2, 3, 4, 6, 8, 11, 12, 18, 20, 26, 29, 39, 39, 54, 54, 69, 73, 94, 89, 119, 118, 144, 145, 185, 169, 225, 215, 259, 258, 317, 291, 378, 357, 423, 410, 511, 457, 588, 547, 639, 626, 764, 679, 861, 792, 933, 896, 1089, 963, 1203, 1112, 1296, 1240, 1495, 1302, 1650

Offset: 4

Author

David W. Wilson

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Column 4 of A282750.

Programs

Mathematica

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 *)

Formula

G.f.: Sum_{k>=1} mu(k)*x^(4*k) / Product_{j=1..4} (1 - x^(j*k)). - Ilya Gutkovskiy, Aug 31 2019

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