A326524 Sum of the smallest parts of the partitions of n into 9 squarefree parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 5, 8, 9, 13, 17, 23, 26, 36, 42, 55, 63, 80, 93, 119, 131, 165, 188, 230, 255, 312, 351, 420, 466, 555, 620, 731, 804, 945, 1046, 1216, 1333, 1550, 1702, 1959, 2141, 2452, 2688, 3064, 3334, 3790, 4136, 4673, 5070

Offset

0,12

Links

Table of n, a(n) for n=0..56.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} mu(q)^2 * mu(p)^2 * mu(o)^2 * mu(m)^2 * mu(l)^2 * mu(k)^2 * mu(j)^2 * mu(i)^2 * mu(n-i-j-k-l-m-o-p-q)^2 * q, where mu is the Möbius function (A008683).

a(n) = A326523(n) - A326525(n) - A326526(n) - A326527(n) - A326528(n) - A326529(n) - A326530(n) - A326531(n) - A326532(n).

Mathematica

Table[Total[Select[IntegerPartitions[n, {9}], AllTrue[#, SquareFreeQ]&][[;; , -1]]], {n, 0, 60}] (* Harvey P. Dale, Mar 22 2023 *)

Crossrefs

Cf. A008683, A326522, A326523, A326525, A326526, A326527, A326528, A326529, A326530, A326531, A326532.

Sequence in context: A326626 A341153 A326628 * A326629 A326445 A069906

Adjacent sequences: A326521 A326522 A326523 * A326525 A326526 A326527

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 11 2019

Status

approved