

A111204


Difference between the closest squares surrounding a squarefree composite number and n have a common divisor greater than 1.


0



7, 9, 9, 9, 11, 13, 15, 15, 15, 15, 15, 15, 15, 17, 19, 21, 21, 21, 21, 21, 21, 21, 21, 21, 23, 25, 25, 25, 25, 25, 27, 27, 27, 27, 27, 27, 27, 27, 27, 29, 31, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 37, 39, 39, 39, 39, 39
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OFFSET

6,1


LINKS



FORMULA

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.


EXAMPLE

14 is a squarefree composite number. 3^2 and 4^2 are the closest squares surrounding 14. So the difference, 169 = 7 and 14 have a common divisor greater than 1 namely 7, so 7 is the first entry in the table.


PROG

(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", ") ) ) ) }


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



