

A069987


Squarefree numbers of form k^2 + 1.


10



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

1,1


COMMENTS

HeathBrown (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


LINKS



FORMULA



MAPLE

select(numtheory:issqrfree, [seq(n^2+1, n=1..100)]); # Robert Israel, Feb 09 2016


MATHEMATICA

Select[ Range[10^4], IntegerQ[ Sqrt[ #  1]] && Union[ Transpose[ FactorInteger[ # ]] [[2]]] [[ 1]] == 1 &]


PROG

(PARI) for(n=1, 100, if(issquarefree(n^2+1), print1(n^2+1, ", ")))


CROSSREFS



KEYWORD

nonn


AUTHOR

Sharon Sela (sharonsela(AT)hotmail.com), May 01 2002


EXTENSIONS



STATUS

approved



