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A069987
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Squarefree numbers of form k^2 + 1.
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10
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2, 5, 10, 17, 26, 37, 65, 82, 101, 122, 145, 170, 197, 226, 257, 290, 362, 401, 442, 485, 530, 577, 626, 677, 730, 785, 842, 901, 962, 1090, 1157, 1226, 1297, 1370, 1522, 1601, 1765, 1937, 2026, 2117, 2210, 2305, 2402, 2501, 2602, 2705, 2810, 2917, 3026
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OFFSET
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1,1
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COMMENTS
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Heath-Brown (following Estermann) shows that, for any e > 0, there are k sqrt(x) + O(x^{7/24 + e}) members of this sequence up to x, for k = Product(1 - 2/p^2) = 0.8948412245... (A335963) where the product is over primes p = 1 mod 4. - Charles R Greathouse IV, Nov 19 2012, corrected by Amiram Eldar, Jul 08 2020
Integers k for which the period of the continued fraction of sqrt(k) is 1. - Michel Marcus, Apr 12 2019
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LINKS
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FORMULA
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MAPLE
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select(numtheory:-issqrfree, [seq(n^2+1, n=1..100)]); # Robert Israel, Feb 09 2016
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MATHEMATICA
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Select[ Range[10^4], IntegerQ[ Sqrt[ # - 1]] && Union[ Transpose[ FactorInteger[ # ]] [[2]]] [[ -1]] == 1 &]
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PROG
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(PARI) for(n=1, 100, if(issquarefree(n^2+1), print1(n^2+1, ", ")))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Sharon Sela (sharonsela(AT)hotmail.com), May 01 2002
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EXTENSIONS
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STATUS
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approved
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