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a(n) = card{ x <= n : bigomega(x) = 4 }.
3

%I #15 Jun 24 2022 23:37:16

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,

%T 2,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,6,6,6,6,7,7,7,7,7,7,7,7,7,

%U 7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,9,9,9,9,10,10,11,11,11,11,11,11,11,11,11,11

%N a(n) = card{ x <= n : bigomega(x) = 4 }.

%H Charles R Greathouse IV, <a href="/A082996/b082996.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) ~ (1/6)*(n/log(n))*log(log(n))^3.

%o (PARI) a(n)=sum(i=1,n,bigomega(i)==4)

%o (PARI) a(n)=my(j,s);forprime(p=2,(n+.5)^(1/4),forprime(q=p,(n/p+.5)^(1/3),j=primepi(q)-2;forprime(r=q,sqrtint(n\(p*q)),s+=primepi(n\(p*q*r))-j++)));s \\ _Charles R Greathouse IV_, Mar 21 2012

%Y Cf. A072000, A072114.

%Y Partial sums of A101637.

%K nonn,easy

%O 1,24

%A _Benoit Cloitre_, May 30 2003