A111204 Difference between the closest squares surrounding a squarefree composite number and n have a common divisor greater than 1.

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

Offset

6,1

Links

Table of n, a(n) for n=6..76.

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, 16-9 = 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

Sequence in context: A199386 A143959 A121313 * A000510 A262310 A167628

Adjacent sequences: A111201 A111202 A111203 * A111205 A111206 A111207

Keyword

easy,nonn

Author

Cino Hilliard, Nov 12 2005

Status

approved