OFFSET
1,2
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = Sum_{i=1..n} mu(floor((2*n - i)/i))^2 * (1 - ceiling((2*n - i)/i) + floor((2*n - i)/i)), where mu is the Möbius function (A008683).
EXAMPLE
a(6) = 5; 2*6 = 12 has five rectangles, 1 X 11, 2 X 10, 3 X 9, 4 X 8 and 6 X 6 such that the ratios 11/1 = 11, 10/2 = 5, 9/3 = 3, 8/4 = 2 and 6/6 = 1 are all squarefree.
MAPLE
f:= proc(n) uses numtheory;
nops(select(r -> r <= n and issqrfree(2*n/r-1) , divisors(2*n), n))
end proc:
map(f, [$1..100]); # Robert Israel, Apr 27 2020
MATHEMATICA
Table[Sum[MoebiusMu[(2 n - i)/i]^2 (1 - Ceiling[(2 n - i)/i] + Floor[(2 n - i)/i]), {i, n}], {n, 100}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Apr 24 2020
STATUS
approved