A101605 a(n) = 1 if n is a product of exactly 3 (not necessarily distinct) primes, otherwise 0.

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

Offset: 1

Author

Jonathan Vos Post, Dec 09 2004

Keywords

• easy
• nonn

Examples

			a(28) = 1 because 28 = 2 * 2 * 7 is the product of exactly 3 primes, counted with multiplicity.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Almost Prime.
• Index entries for characteristic functions
• Index entries for sequences computed from exponents in factorization of n

Crossrefs

Cf. A010051, A064911, (char funct. of) A014612, A101637, A123074.

Programs

Maple

A101605 := proc(n)
    if numtheory[bigomega](n) = 3 then
        1;
    else
        0;
    end if;
end proc: # R. J. Mathar, Mar 13 2015

Mathematica

Table[Boole[PrimeOmega[n] == 3], {n, 100}] (* Jean-François Alcover, Mar 23 2020 *)

PARI

is(n)=bigomega(n)==3 \\ Charles R Greathouse IV, Apr 25 2016

Formula

a(n) = 1 if n has exactly three prime factors (not necessarily distinct), else a(n) = 0. a(n) = 1 if n is an element of A014612, else a(n) = 0.

a(n) = floor(Omega(n)/3) * floor(3/Omega(n)). - Wesley Ivan Hurt, Jan 10 2013

Extensions

Description clarified by Antti Karttunen, Jul 23 2017