A056912 Odd squarefree numbers for which the number of prime divisors is odd.

3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 105, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 165, 167, 173, 179, 181, 191, 193, 195, 197, 199, 211, 223, 227, 229, 231, 233, 239, 241, 251, 255

Offset

1,1

Comments

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

m is a term iff mu(m)^m < 0 (A080323(a(n))<0), where mu is the Moebius function (A008683). - Reinhard Zumkeller, Feb 14 2003

The asymptotic density of this sequence is 2/Pi^2 (A185197). - Amiram Eldar, Oct 06 2020

References

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

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]

Example

a(27) = 3*5*7 = 105 is the least nonprime.

Mathematica

Select[Range[3, 300], SquareFreeQ[#] && LiouvilleLambda[#] == -1 &] (* Jean-François Alcover, Jul 30 2013 *)
Select[Range[1, 255, 2], MoebiusMu[#] == -1 &] (* Amiram Eldar, Oct 06 2020 *)

Prog

(PARI) isok(n) = (n%2) && issquarefree(n) && (omega(n)%2) \\ Michel Marcus, Jun 15 2013
(PARI) is(n)=if(n%2, my(f=factor(n)[, 2]); n>1 && vecmax(f)<2 && #f%2, 0) \\ Charles R Greathouse IV, Jun 15 2013

Crossrefs

Cf. A056911, A056913, A008836, A026424, A028260, A185197.

Sequence in context: A330225 A275938 A093893 * A075763 A074918 A175524

Adjacent sequences: A056909 A056910 A056911 * A056913 A056914 A056915

Keyword

easy,nonn

Author

James A. Sellers, Jul 07 2000

Status

approved