OFFSET
0,10
LINKS
FORMULA
a(n) = Sum_{o=1..floor(n/7)} Sum_{m=o..floor((n-o)/6)} Sum_{l=m..floor((n-m-o)/5)} Sum_{k=l..floor((n-l-m-o)/4)} Sum_{j=k..floor((n-k-l-m-o)/3} Sum_{i=j..floor((n-j-k-l-m-o)/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)^2, where mu is the Möbius function (A008683).
a(n) = A308953(n)/n for n > 0.
MAPLE
g:= proc(n, k, m) option remember; local i , j;
if m=1 then if n=k then return 1 else return 0 fi fi;
if k*m < n then return 0 fi;
if k*m = n then return 1 fi;
add(add(procname(n-i*k, j, m-i), j= select(numtheory:-issqrfree, [$max(1, ceil((n-i*k)/(m-i))) .. k-1])), i=1..min(n/k, m-1));
end proc:
f:= proc(n) local k;
add(g(n, k, 7), k=select(numtheory:-issqrfree, [$ceil(n/7)..n]))
end proc:
f(0):= 0:
map(f, [$0..100]); # Robert Israel, Jul 03 2019
MATHEMATICA
Table[Sum[Sum[Sum[Sum[Sum[Sum[MoebiusMu[o]^2 * MoebiusMu[m]^2 * MoebiusMu[l]^2 * MoebiusMu[k]^2 * MoebiusMu[j]^2 * MoebiusMu[i]^2 * MoebiusMu[n - i - j - k - l - m - o]^2, {i, j, Floor[(n - j - k - l - m - o)/2]}], {j, k, Floor[(n - k - l - m - o)/3]}], {k, l, Floor[(n - l - m - o)/4]}], {l, m, Floor[(n - m - o)/5]}], {m, o, Floor[(n - o)/6]}], {o, Floor[n/7]}], {n, 0, 50}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jul 03 2019
STATUS
approved