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

%I A101605 #41 Feb 16 2025 08:32:55
%S A101605 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,
%T A101605 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,
%U A101605 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
%N A101605 a(n) = 1 if n is a product of exactly 3 (not necessarily distinct) primes, otherwise 0.
%H A101605 Antti Karttunen, <a href="/A101605/b101605.txt">Table of n, a(n) for n = 1..10000</a>
%H A101605 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AlmostPrime.html">Almost Prime</a>.
%H A101605 <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%H A101605 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F A101605 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.
%F A101605 a(n) = floor(Omega(n)/3) * floor(3/Omega(n)). - _Wesley Ivan Hurt_, Jan 10 2013
%e A101605 a(28) = 1 because 28 = 2 * 2 * 7 is the product of exactly 3 primes, counted with multiplicity.
%p A101605 A101605 := proc(n)
%p A101605     if numtheory[bigomega](n) = 3 then
%p A101605         1;
%p A101605     else
%p A101605         0;
%p A101605     end if;
%p A101605 end proc: # _R. J. Mathar_, Mar 13 2015
%t A101605 Table[Boole[PrimeOmega[n] == 3], {n, 100}] (* _Jean-François Alcover_, Mar 23 2020 *)
%o A101605 (PARI) is(n)=bigomega(n)==3 \\ _Charles R Greathouse IV_, Apr 25 2016
%Y A101605 Cf. A010051, A064911, (char funct. of) A014612, A101637, A123074.
%K A101605 easy,nonn
%O A101605 1,1
%A A101605 _Jonathan Vos Post_, Dec 09 2004
%E A101605 Description clarified by _Antti Karttunen_, Jul 23 2017