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A082996 a(n) = card{ x <= n : bigomega(x) = 4 }.

%I A082996 #18 Mar 29 2025 15:40:23
%S A082996 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 A082996 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 A082996 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 A082996 a(n) = card{ x <= n : bigomega(x) = 4 }.
%H A082996 Charles R Greathouse IV, <a href="/A082996/b082996.txt">Table of n, a(n) for n = 1..10000</a>
%F A082996 a(n) ~ (1/6)*(n/log(n))*log(log(n))^3.
%o A082996 (PARI) a(n)=sum(i=1,n,bigomega(i)==4)
%o A082996 (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
%o A082996 (Python)
%o A082996 from math import isqrt
%o A082996 from sympy import primepi, primerange, integer_nthroot
%o A082996 def A082996(n): return int(sum(primepi(n//(k*m*r))-c for a,k in enumerate(primerange(integer_nthroot(n,4)[0]+1)) for b,m in enumerate(primerange(k,integer_nthroot(n//k,3)[0]+1),a) for c,r in enumerate(primerange(m,isqrt(n//(k*m))+1),b))) # _Chai Wah Wu_, Mar 29 2025
%Y A082996 Cf. A072000, A072114.
%Y A082996 Partial sums of A101637.
%K A082996 nonn,easy
%O A082996 1,24
%A A082996 _Benoit Cloitre_, May 30 2003