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%I #7 Oct 01 2013 17:58:20
%S 7,9,9,9,11,13,15,15,15,15,15,15,15,17,19,21,21,21,21,21,21,21,21,21,
%T 23,25,25,25,25,25,27,27,27,27,27,27,27,27,27,29,31,33,33,33,33,33,33,
%U 33,33,33,33,33,33,33,35,35,35,35,35,35,35,35,35,35,35,37,39,39,39,39,39
%N Difference between the closest squares surrounding a squarefree composite number and n have a common divisor greater than 1.
%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. If gcd(n, d) > 1 then list d.
%e 14 is a squarefree composite number. 3^2 and 4^2 are the closest squares surrounding 14. So the difference, 16-9 = 7 and 14 have a common divisor greater than 1 namely 7, so 7 is the first entry in the table.
%o (PARI) surrsqgcd(n) = { local(x,y,j,r,d); for(x=1,n, if(!issquare(x)&!isprime(x), r=floor(sqrt(x)); d=r+r+1; if(gcd(x,d) > 1, print1(d",") ) ) ) }
%K easy,nonn
%O 6,1
%A _Cino Hilliard_, Nov 12 2005
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