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A117206
Squarefree positive integers k such that 2*k-1 is also squarefree.
3
1, 2, 3, 6, 7, 10, 11, 15, 17, 19, 21, 22, 26, 29, 30, 31, 33, 34, 35, 37, 39, 42, 43, 46, 47, 51, 53, 55, 57, 58, 62, 65, 66, 67, 69, 70, 71, 73, 78, 79, 82, 83, 87, 89, 91, 93, 94, 97, 101, 102, 103, 105, 106, 107, 109, 110, 111, 114, 115, 118, 119, 127, 129, 130, 133
OFFSET
1,2
COMMENTS
The asymptotic density of this sequence is (3/2)*A065474 = 0.4839511484... (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) = (A117205(n) + 1)/2.
EXAMPLE
10 and 2*10 - 1 = 19 are both squarefree, so 10 is in the sequence.
MAPLE
with(numtheory): a:=proc(n) if abs(mobius(n))>0 and abs(mobius(2*n-1))>0 then n else fi end: seq(a(n), n=1..160); # Emeric Deutsch, Mar 08 2006
MATHEMATICA
Select[Range[200], And@@SquareFreeQ/@{#, 2#-1}&] (* Harvey P. Dale, Dec 17 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Mar 02 2006
EXTENSIONS
More terms from Emeric Deutsch, Mar 08 2006
STATUS
approved