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A030230
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Numbers that have an odd number of distinct prime divisors.
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19
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2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 30, 31, 32, 37, 41, 42, 43, 47, 49, 53, 59, 60, 61, 64, 66, 67, 70, 71, 73, 78, 79, 81, 83, 84, 89, 90, 97, 101, 102, 103, 105, 107, 109, 110, 113, 114, 120, 121, 125, 126, 127, 128, 130, 131, 132, 137, 138, 139, 140, 149
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OFFSET
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1,1
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..1000
Mats Granvik, Mathematica program to compute the relation to the Dirichlet inverse of the Euler totient function
H. Helfgott and A. Ubis, Primos, paridad y análisis, arXiv:1812.08707 [math.NT], Dec. 2018.
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FORMULA
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From Benoit Cloitre, Dec 08 2002: (Start)
k such that Sum_{d|k} mu(d)*tau(d) = (-1)^omega(k) = -1 where mu(d) = A008683(d), tau(d) = A000005(d) and omega(d) = A001221(d).
k such that A023900(k) < 0. (End)
gcd(A008472(a(n)), A007947(a(n))) > 1; see A014963. - Labos Elemer, Mar 26 2003
A076479(a(n)) = -1. - Reinhard Zumkeller, Jun 01 2013
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MAPLE
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q:= n-> is(nops(ifactors(n)[2])::odd):
select(q, [$1..150])[]; # Alois P. Heinz, Feb 12 2021
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MATHEMATICA
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(* Prior to version 7.0 *) littleOmega[n_] := Length[FactorInteger[n]]; Select[ Range[2, 149], (-1)^littleOmega[#] == -1 &] (* Jean-François Alcover, Nov 30 2011, after Benoit Cloitre *)
(* Version 7.0+ *) Select[Range[2, 149], (-1)^PrimeNu[#] == -1 &]
Select[Range[1000], OddQ[PrimeNu[#]]&] (* Harvey P. Dale, Nov 27 2012 *)
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PROG
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(Haskell)
a030230 n = a030230_list !! (n-1)
a030230_list = filter (odd . a001221) [1..]
-- Reinhard Zumkeller, Aug 14 2011
(PARI) is(n)=omega(n)%2 \\ Charles R Greathouse IV, Sep 14 2015
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CROSSREFS
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Cf. A030231, A123066.
Cf. A008472, A007947, A014963.
Cf. A076479.
Cf. A008683, A000005, A001221, A023900.
Sequence in context: A331912 A326848 A328957 * A089352 A086486 A071139
Adjacent sequences: A030227 A030228 A030229 * A030231 A030232 A030233
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KEYWORD
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nonn,easy,nice
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AUTHOR
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David W. Wilson
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STATUS
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approved
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