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A111205 Squarefree numbers n such that the difference between the closest squares surrounding n and n have a common divisor greater than 1. 0
14, 18, 21, 24, 33, 39, 50, 51, 54, 55, 57, 60, 63, 68, 95, 102, 105, 108, 111, 112, 114, 117, 119, 120, 138, 145, 150, 155, 160, 165, 171, 174, 177, 180, 183, 186, 189, 192, 195, 203, 248, 258, 261, 264, 267, 270, 273, 275, 276, 279, 282, 285, 286, 288, 290 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,1

COMMENTS

Conjecture: The number of terms in this sequence is infinite.

LINKS

Table of n, a(n) for n=6..60.

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 n.

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 14 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(x", ") ) )) }

CROSSREFS

Sequence in context: A052026 A317743 A118499 * A097324 A051419 A000053

Adjacent sequences:  A111202 A111203 A111204 * A111206 A111207 A111208

KEYWORD

easy,nonn

AUTHOR

Cino Hilliard, Nov 12 2005

STATUS

approved

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Last modified August 14 05:03 EDT 2022. Contains 356110 sequences. (Running on oeis4.)