OFFSET
1,2
COMMENTS
The asymptotic density of this sequence is (3/4)*A065474 = 0.2419755742... (Erdős and Ivić, 1987). - Amiram Eldar, Feb 17 2021
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Paul Erdős and Aleksandar Ivić, The distribution of values of a certain class of arithmetic functions at consecutive integers, Colloq. Math. Soc. János Bolyai, Vol. 51 (1987), pp. 45-91.
FORMULA
a(n) = 2 * A117206(n) - 1.
EXAMPLE
21 and (21+1)/2 = 11 are both squarefree, so 21 is in the sequence.
MAPLE
with(numtheory): a:=proc(n) if n mod 2 =1 and abs(mobius(n))>0 and abs(mobius((n+1)/2))>0 then n else fi end: seq(a(n), n=1..300); # Emeric Deutsch, Mar 07 2006
MATHEMATICA
Select[Range[1, 301, 2], And@@(SquareFreeQ/@{#, (#+1)/2})&] (* Harvey P. Dale, Jul 30 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Mar 02 2006
EXTENSIONS
More terms from Emeric Deutsch, Mar 07 2006
STATUS
approved