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A049533 Numbers n such that n^2+1 is squarefree. 4
1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 39, 40, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A059592(n) = 1; cf. A069987. - Reinhard Zumkeller, Nov 08 2006

Complement of A049532.

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000

EXAMPLE

10 is a member because 10^2+1=100+1=101 is squarefree.

Reasons why certain numbers are excluded: 7^2+1 = 2*5^2, 18^2+1 = 13*5^2, 32^2+1 = 41*5^2, 38^2+1 = 5*17^2, 41^2+1 = 2*29^2, 43^2+1 = 74*5^2, 57^2+1 = 130*5^2, 82^2+1 = 269*5^2. - Neven Juric, Oct 06 2008

MATHEMATICA

Select[Range@ 80, SquareFreeQ[#^2 + 1] &] (* Michael De Vlieger, Aug 09 2017 *)

PROG

(MAGMA) [ n: n in [1..100] | IsSquarefree(n^2+1) ]; // Vincenzo Librandi, Dec 25 2010

(PARI) isok(n) = issquarefree(n^2+1); \\ Michel Marcus, Feb 09 2016

CROSSREFS

Cf. A049532, A059592, A069987.

Sequence in context: A129618 A038673 A183219 * A052419 A257458 A179439

Adjacent sequences:  A049530 A049531 A049532 * A049534 A049535 A049536

KEYWORD

nonn,changed

AUTHOR

Labos Elemer

STATUS

approved

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Last modified August 19 07:12 EDT 2017. Contains 290794 sequences.