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A056912 Odd squarefree numbers for which the number of prime divisors is odd. 7
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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A330225 A275938 A093893 * A075763 A074918 A175524
KEYWORD
easy,nonn
AUTHOR
James A. Sellers, Jul 07 2000
STATUS
approved

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Last modified April 20 12:18 EDT 2024. Contains 371839 sequences. (Running on oeis4.)