OFFSET
0,12
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).
MATHEMATICA
Table[Total[Select[IntegerPartitions[n, {9}], AllTrue[#, SquareFreeQ]&][[;; , -1]]], {n, 0, 60}] (* Harvey P. Dale, Mar 22 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jul 11 2019
STATUS
approved