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a(n) = 1 if n is a 4-almost prime, that is a product of exactly four (not necessarily distinct) primes, 0 otherwise.
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%I #22 Sep 13 2024 17:52:08

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,

%T 0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1

%N a(n) = 1 if n is a 4-almost prime, that is a product of exactly four (not necessarily distinct) primes, 0 otherwise.

%C Characteristic function of A014613.

%C See A101638 for the inverse Moebius transform of this sequence.

%H Antti Karttunen, <a href="/A101637/b101637.txt">Table of n, a(n) for n = 1..65537</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Almostprime.html">Almost Prime.</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>

%e a(100) = 1 because 100 = 2 * 2 * 5 * 5 is the product of exactly 4 primes and thus is a 4-almost prime.

%t Table[If[PrimeOmega[n]==4,1,0],{n,100}] (* _Harvey P. Dale_, Sep 13 2024 *)

%o (PARI) a(n)=bigomega(n)==4 \\ _Charles R Greathouse IV_, Jan 31 2017

%Y Cf. A101638, A014613, A000040, A001358, A014612, A014614.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Dec 10 2004

%E Name edited by _Antti Karttunen_, Oct 08 2017