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Search: id:A111204
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| A111204 |
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Difference between the closest squares surrounding a squarefree composite number and n have a common divisor greater than 1. |
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+0
1
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| 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; listen)
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OFFSET
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6,1
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FORMULA
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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.
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EXAMPLE
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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.
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PROGRAM
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(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", ") ) ) ) }
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CROSSREFS
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Sequence in context: A021930 A143959 A121313 this_sequence A000510 A167628 A112954
Adjacent sequences: A111201 A111202 A111203 this_sequence A111205 A111206 A111207
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Nov 12 2005
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