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 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 7 17:47 EDT 2024. Contains 375017 sequences. (Running on oeis4.)