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A030231 Number of distinct primes dividing n is even. 15
1, 6, 10, 12, 14, 15, 18, 20, 21, 22, 24, 26, 28, 33, 34, 35, 36, 38, 39, 40, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 62, 63, 65, 68, 69, 72, 74, 75, 76, 77, 80, 82, 85, 86, 87, 88, 91, 92, 93, 94, 95, 96, 98, 99, 100, 104, 106, 108, 111, 112, 115, 116, 117, 118, 119 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Gcd(A008472(a(n)), A007947(a(n)))=1; see A014963. - Labos Elemer, Mar 26 2003

Superset of A007774. - R. J. Mathar, Oct 23 2008

A076479(a(n)) = +1. - Reinhard Zumkeller, Jun 01 2013

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

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)

MATHEMATICA

Select[Range[200], EvenQ[PrimeNu[#]]&] (* Harvey P. Dale, Jun 22 2011 *)

PROG

(PARI) j=[]; for(n=1, 200, x=omega(n); if(Mod(x, 2)==0, j=concat(j, n))); j

(PARI) is(n)=omega(n)%2==0 \\ Charles R Greathouse IV, Sep 14 2015

(Haskell)

a030231 n = a030231_list !! (n-1)

a030231_list = filter (even . a001221) [1..]

-- Reinhard Zumkeller, Mar 26 2013

CROSSREFS

Cf. A028260, A030230, A123066.

Cf. A008472, A007947, A014963.

Cf. A007774, A076479.

Cf. A008683, A000005, A001221, A023900.

Sequence in context: A323304 A106543 A007774 * A267114 A275665 A056760

Adjacent sequences:  A030228 A030229 A030230 * A030232 A030233 A030234

KEYWORD

nonn,easy,nice

AUTHOR

David W. Wilson

EXTENSIONS

Corrected by Dan Pritikin (pritikd(AT)muohio.edu), May 29 2002

STATUS

approved

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Last modified January 19 20:01 EST 2019. Contains 319309 sequences. (Running on oeis4.)