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%I #32 Sep 08 2022 08:45:01
%S 1,15,21,33,35,39,51,55,57,65,69,77,85,87,91,93,95,111,115,119,123,
%T 129,133,141,143,145,155,159,161,177,183,185,187,201,203,205,209,213,
%U 215,217,219,221,235,237,247,249,253,259,265,267,287,291,295,299,301,303
%N Odd squarefree numbers for which the number of prime divisors is even.
%C Liouville function lambda(n) (A008836) is positive.
%C From _Peter Munn_, Jan 16 2020: (Start)
%C The sequence is closed under the commutative binary operation A059897(.,.). As integers are self-inverse under A059897, it forms a subgroup of the positive integers considered as a group under A059897.
%C This sequence is the intersection of A000379 and A056911, which are also subgroups of the positive integers under A059897.
%C (End)
%C The asymptotic density of this sequence is 2/Pi^2 (A185197). - _Amiram Eldar_, Oct 06 2020
%H Charles R Greathouse IV, <a href="/A056913/b056913.txt">Table of n, a(n) for n = 1..10000</a>
%H H. Gupta, <a href="/A002556/a002556.pdf"> A formula for L(n)</a>, J. Indian Math. Soc., 7 (1943), 68-71. [Annotated scanned copy]
%t f[n_]:=Last/@FactorInteger[n]=={1,1}&&FactorInteger[n][[1,1]]>2; a=6;lst={1};Do[If[f[n],AppendTo[lst,n]],{n,6!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 23 2009 *)
%t Select[Range[1, 303, 2], MoebiusMu[#] == 1 &] (* _Amiram Eldar_, Oct 06 2020 *)
%o (PARI) list(lim)=my(v=List([1])); forfactored(n=15,lim\1, if(n[2][1,1]>2 && vecmax(n[2][,2])==1 && #(n[2][,2])%2==0, listput(v,n[1]))); Vec(v) \\ _Charles R Greathouse IV_, Nov 05 2017
%o (Magma) [k:k in [1..303 by 2]| IsSquarefree(k) and IsEven(#PrimeDivisors(k))]; // _Marius A. Burtea_, Jan 21 2020
%Y Intersection of A056911 with either of A000379, A028260.
%Y Cf. A056912, A059897, A008836, A026424, A185197.
%K easy,nonn
%O 1,2
%A _James A. Sellers_, Jul 07 2000
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