login
This site is supported by donations to The OEIS Foundation.

 

Logo

"Email this user" was broken Aug 14 to 9am Aug 16. If you sent someone a message in this period, please send it again.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A069987 Squarefree numbers of form n^2 + 1. 8
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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 = prod(1 - 2/p^2)/2 = 0.4474206122... where the product is over primes p = 1 mod 4. - Charles R Greathouse IV, Nov 19 2012

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

T. Estermann, Einige Sätze über quadratfreie Zahlen, Math. Ann. 105 (1931), pp. 653-662.

D. R. Heath-Brown, Square-free values of n^2 + 1, Acta Arithmetica 155 (2012), pp. 1-13. arXiv:1010.6217

FORMULA

a(n) = A049533(n)^2+1.

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 &]

Select[Range[60]^2+1, SquareFreeQ] (* Harvey P. Dale, Mar 21 2013 *)

PROG

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

CROSSREFS

Cf. A059591, A002496, A124809, A005117, A002522.

Sequence in context: A002522 A217990 A248193 * A248742 A246884 A119114

Adjacent sequences:  A069984 A069985 A069986 * A069988 A069989 A069990

KEYWORD

nonn

AUTHOR

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

EXTENSIONS

Edited and extended by Robert G. Wilson v, Benoit Cloitre and Vladeta Jovovic, May 04 2002

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified August 20 03:34 EDT 2017. Contains 290823 sequences.