%I #6 Oct 01 2013 17:58:20

%S 5,5,7,7,7,7,9,9,9,9,9,11,11,11,11,11,11,11,11,13,13,13,13,13,13,13,

%T 13,15,15,15,15,15,15,15,15,15,15,15,17,17,17,17,17,17,17,17,17,17,17,

%U 17,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19

%N Difference between the closest squares surrounding squarefree composite numbers.

%F Let n be a squarefree composite number and r = floor(sqrt(n)). Then the closest surrounding squares of n are r^2 and (r+1)^2. So d = (r+1)^2 - r^2 = 2r+1.

%e 6 is the first positive squarefree composite number. 2^2 and 3^2 are the closest squares surrounding 6. So the difference, 9-4 = 5, is the first entry in the table.

%o (PARI) surrsq(n) = { local(x,y,j,r,d); for(x=1,n, if(!issquare(x)&!isprime(x), r=floor(sqrt(x)); d=r+r+1; print1(d",") \ print1(r^2","(r+1)^2",") ) ) }

%K easy,nonn

%O 6,1

%A _Cino Hilliard_, Nov 12 2005