OFFSET
0,9
LINKS
FORMULA
a(n) = Sum_{p=1..floor(n/8)} Sum_{o=p..floor((n-p)/7)} Sum_{m=o..floor((n-o-p)/6)} Sum_{l=m..floor((n-m-o-p)/5)} Sum_{k=l..floor((n-l-m-o-p)/4)} Sum_{j=k..floor((n-k-l-m-o-p)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p)/2)} (i * mu(i)^2 + j * mu(j)^2 + k * mu(k)^2 + l * mu(l)^2 + m * mu(m)^2 + o * mu(o)^2 + p * mu(p)^2 + (n-i-j-k-l-m-o-p) * mu(n-i-j-k-l-m-o-p)^2), where mu is the Möbius function (A008683).
MATHEMATICA
Table[Total[Select[Flatten[IntegerPartitions[n, {8}]], SquareFreeQ]], {n, 0, 50}] (* Harvey P. Dale, Jun 10 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Aug 04 2019
STATUS
approved