

A056913


Odd squarefree numbers for which the number of prime divisors is even.


15



1, 15, 21, 33, 35, 39, 51, 55, 57, 65, 69, 77, 85, 87, 91, 93, 95, 111, 115, 119, 123, 129, 133, 141, 143, 145, 155, 159, 161, 177, 183, 185, 187, 201, 203, 205, 209, 213, 215, 217, 219, 221, 235, 237, 247, 249, 253, 259, 265, 267, 287, 291, 295, 299, 301, 303
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OFFSET

1,2


COMMENTS

Liouville function lambda(n) (A008836) is positive.
The sequence is closed under the commutative binary operation A059897(.,.). As integers are selfinverse under A059897, it forms a subgroup of the positive integers considered as a group under A059897.
This sequence is the intersection of A000379 and A056911, which are also subgroups of the positive integers under A059897.
(End)


LINKS

H. Gupta, A formula for L(n), J. Indian Math. Soc., 7 (1943), 6871. [Annotated scanned copy]


MATHEMATICA

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 *)
Select[Range[1, 303, 2], MoebiusMu[#] == 1 &] (* Amiram Eldar, Oct 06 2020 *)


PROG

(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
(Magma) [k:k in [1..303 by 2] IsSquarefree(k) and IsEven(#PrimeDivisors(k))]; // Marius A. Burtea, Jan 21 2020


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



