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A030230 Numbers n such that number of distinct primes dividing n is odd. 16
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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.

FORMULA

From Benoit Cloitre, Dec 08 2002: (Start)

n such that Sum_{d|n} mu(d)*tau(d) = (-1)^omega(n) = -1 where mu(d) = A008683(d), tau(d) = A000005(d) and omega(d) = A001221(d).

n such that A023900(n) < 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

MATHEMATICA

(* 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 *)

PROG

(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

CROSSREFS

Cf. A030231, A123066.

Cf. A008472, A007947, A014963.

Cf. A076479.

Cf. A008683, A000005, A001221, A023900.

Sequence in context: A302040 A302036 A326848 * A089352 A086486 A071139

Adjacent sequences:  A030227 A030228 A030229 * A030231 A030232 A030233

KEYWORD

nonn,easy,nice

AUTHOR

David W. Wilson

STATUS

approved

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Last modified October 15 01:40 EDT 2019. Contains 328025 sequences. (Running on oeis4.)