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A056913 Odd squarefree numbers for which the number of prime divisors is even. 8
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Liouville function lambda(n) (A008836) is positive.

From Peter Munn, Jan 16 2020: (Start)

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.

This sequence is the intersection of A000379 and A056911, which are also subgroups of the positive integers under A059897.

(End)

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

H. Gupta, A formula for L(n), J. Indian Math. Soc., 7 (1943), 68-71. [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 *)

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

Intersection of A056911 with either of A000379, A028260.

Cf. A056912, A059897, A008836, A026424.

Sequence in context: A146166 A024556 A046388 * A002557 A128907 A321644

Adjacent sequences:  A056910 A056911 A056912 * A056914 A056915 A056916

KEYWORD

easy,nonn

AUTHOR

James A. Sellers, Jul 07 2000

STATUS

approved

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Last modified July 12 12:18 EDT 2020. Contains 335661 sequences. (Running on oeis4.)