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A122132 Squarefree numbers multiplied by binary powers.

%I A122132 #38 Sep 22 2020 02:42:16
%S A122132 1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,19,20,21,22,23,24,26,28,29,
%T A122132 30,31,32,33,34,35,37,38,39,40,41,42,43,44,46,47,48,51,52,53,55,56,57,
%U A122132 58,59,60,61,62,64,65,66,67,68,69,70,71,73,74,76,77,78,79,80,82,83,84,85
%N A122132 Squarefree numbers multiplied by binary powers.
%C A122132 These numbers are called "oddly squarefree" in Banks and Luca. - _Michel Marcus_, Mar 14 2016
%C A122132 The asymptotic density of this sequence is 8/Pi^2 (A217739). - _Amiram Eldar_, Sep 21 2020
%H A122132 Reinhard Zumkeller, <a href="/A122132/b122132.txt">Table of n, a(n) for n = 1..10000</a>
%H A122132 William D. Banks and Florian Luca, <a href="http://dx.doi.org/10.4064/aa120-3-1">Roughly squarefree values of the Euler and Carmichael functions</a>, Acta Arithmetica, Vol. 120, No. 3 (2005), pp. 211-230.
%F A122132 a(n) = A007947(a(n)) * A006519(a(n)) / (2 - a(n) mod 2);
%F A122132 A007947(a(n)) = A000265(a(n)) * (2 - a(n) mod 2).
%F A122132 A008966(A000265(a(n))) = 1. - _Reinhard Zumkeller_, Jan 24 2012
%F A122132 A010052(A008477(a(n))) = 1. - _Reinhard Zumkeller_, Feb 17 2012
%t A122132 Select[Range@ 85, SquareFreeQ[#/2^IntegerExponent[#, 2]] &] (* _Michael De Vlieger_, Mar 15 2020 *)
%o A122132 (Haskell)
%o A122132 a122132 n = a122132_list !! (n-1)
%o A122132 a122132_list = filter ((== 1) . a008966 . a000265) [1..]
%o A122132 -- _Reinhard Zumkeller_, Jan 24 2012
%o A122132 (PARI) is(n)=issquarefree(n>>valuation(n,2)); \\ _Charles R Greathouse IV_, Sep 02 2015
%Y A122132 Subsequences: A000079, A005117, A007283, A051916, A056911, A029747.
%Y A122132 Complement: A038838.
%Y A122132 Cf. A217739.
%K A122132 nonn,easy
%O A122132 1,2
%A A122132 _Reinhard Zumkeller_, Aug 21 2006