A066247 Characteristic function of composite numbers: 1 if n is composite else 0.

0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1

Offset

1,1

Comments

a(n) = signum(A066246(n)), where signum = A057427. For n > 1: a(n) = 1 - A010051(n) = A005171(n).

a(n) = A057427(A086971(n)). - Reinhard Zumkeller, Dec 14 2012

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions

Index entries for sequences computed from exponents in factorization of n

Formula

For n>1 a(n) = 1-floor(1/A001222(n)). - Enrique Pérez Herrero, Aug 08 2012

a(n) = A065855(n)-A065855(n-1) = 1-A000720(n)+A000720(n-1). - Chayim Lowen, Jul 23 2015

Dirichlet g.f.: Sum_{n>=1} a(n)/n^s = Zeta(s)-1-P(s), where P is prime zeta. - Enrique Pérez Herrero, Aug 08 2012

a(n) = 1 if A001222(n) > 1, 0 otherwise. - Antti Karttunen, Nov 20 2017

Mathematica

A066247[n_]:=1-Boole[PrimeQ[n]]-KroneckerDelta[n, 1] (* Enrique Pérez Herrero, Oct 13 2010 *)
Table[Boole[CompositeQ[n]], {n, 1, 105}] (* Jean-François Alcover, Jan 25 2018 *)

Prog

(PARI) a(n)=!isprime(n)&&n>1 \\ Charles R Greathouse IV, Aug 21 2011
(Haskell)
a066247 1 = 0
a066247 n = 1 - a010051 n  -- Reinhard Zumkeller, Feb 04 2012

Crossrefs

Cf. A001222, A002808, A010051, A005171.

Cf. A065855 (partial sums).

Sequence in context: A106002 A341612 A252742 * A379238 A151774 A095792

Adjacent sequences: A066244 A066245 A066246 * A066248 A066249 A066250

Keyword

nonn,easy

Author

Reinhard Zumkeller, Dec 09 2001

Status

approved