OFFSET
0,9
FORMULA
a(n) = Sum_{m=1..floor(n/6)} Sum_{l=m..floor((n-m)/5)} Sum_{k=l..floor((n-l-m)/4)} Sum_{j=k..floor((n-k-l-m)/3)} Sum_{i=j..floor((n-j-k-l-m)/2)} mu(m)^2 * mu(l)^2 * mu(k)^2 * mu(j)^2 * mu(i)^2 * mu(n-i-k-j-l-m)^2 * j, where mu is the Möbius function (A008683).
MATHEMATICA
Table[Total[Select[IntegerPartitions[n, {6}], AllTrue[#, SquareFreeQ]&][[All, 3]]], {n, 0, 60}] (* Harvey P. Dale, Jan 31 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 29 2019
STATUS
approved