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A023024 Number of partitions of n into 4 unordered relatively prime parts. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,3

LINKS

Table of n, a(n) for n=4..61.

Index entries for sequences related to partitions

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

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 *)

CROSSREFS

Column 4 of A282750.

Sequence in context: A034034 A263132 A018502 * A018362 A033056 A060469

Adjacent sequences:  A023021 A023022 A023023 * A023025 A023026 A023027

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified July 27 12:10 EDT 2021. Contains 346306 sequences. (Running on oeis4.)