OFFSET

6,1

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.

EXAMPLE

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.

PROG

(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", ") ) ) }

CROSSREFS

KEYWORD

easy,nonn

AUTHOR

Cino Hilliard, Nov 12 2005

STATUS

approved