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A117205
Odd squarefree positive integers k such that (k+1)/2 is also squarefree.
3
1, 3, 5, 11, 13, 19, 21, 29, 33, 37, 41, 43, 51, 57, 59, 61, 65, 67, 69, 73, 77, 83, 85, 91, 93, 101, 105, 109, 113, 115, 123, 129, 131, 133, 137, 139, 141, 145, 155, 157, 163, 165, 173, 177, 181, 185, 187, 193, 201, 203, 205, 209, 211, 213, 217, 219, 221, 227, 229
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
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