

A067874


Positive integers x satisfying x^2  D*y^2 = 1 for a unique integer D.


6



2, 4, 6, 12, 14, 16, 18, 20, 22, 30, 32, 34, 36, 38, 40, 42, 52, 54, 56, 58, 60, 66, 68, 70, 72, 78, 84, 86, 88, 90, 92, 94, 96, 102, 104, 106, 108, 110, 112, 114, 128, 130, 132, 138, 140, 142, 144, 150, 156, 158, 160, 162, 164, 166, 178, 180, 182, 184, 186, 192, 194, 196, 198
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OFFSET

1,1


COMMENTS

D is unique iff x^2  1 is squarefree, in which case it follows with necessity that D=x^21 and y=1.
All terms are even. A014574 is a subsequence.
Conjecture: All terms of A002110 > 1 are a subsequence.  Griffin N. Macris, Apr 11 2016
All n such that n+1 and n1 are in A056911.  Robert Israel, Apr 12 2016
Numbers with a squarefree neighbor.  JuriStepan Gerasimov, Jan 17 2017


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000


FORMULA

a(n) = 2*A272799(n).  JuriStepan Gerasimov, Jan 17 2017.


MAPLE

select(t > numtheory:issqrfree(t^21), [seq(n, n=2..1000, 2)]); # Robert Israel, Apr 12 2016


MATHEMATICA

Select[Range[200], SquareFreeQ[#^21]&] (* Vladimir Joseph Stephan Orlovsky, Oct 26 2009 *)


PROG

(MAGMA) [n: n in [1..110]  IsSquarefree(n1) and IsSquarefree(n+1)]; \\ JuriStepan Gerasimov, Jan 17 2017


CROSSREFS

Cf. A002110, A005117, A014574, A056911, A226993, A272799, A280892.
Sequence in context: A062856 A056371 A271822 * A015733 A247460 A023187
Adjacent sequences: A067871 A067872 A067873 * A067875 A067876 A067877


KEYWORD

nice,nonn


AUTHOR

Lekraj Beedassy, Feb 25 2002


EXTENSIONS

Corrected and extended by Max Alekseyev, Apr 26 2009
Further edited by Max Alekseyev, Apr 28 2009


STATUS

approved



