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

Author

Reinhard Zumkeller, Dec 09 2001

Keywords

• nonn
• easy

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

Crossrefs

Cf. A001222, A002808, A010051, A005171.

Cf. A065855 (partial sums).

Programs

Haskell

a066247 1 = 0
a066247 n = 1 - a010051 n  -- Reinhard Zumkeller, Feb 04 2012

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 *)

PARI

a(n)=!isprime(n)&&n>1 \\ Charles R Greathouse IV, Aug 21 2011

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