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

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, 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, 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

Offset

1,24

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

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

Prog

(PARI) a(n)=sum(i=1, n, bigomega(i)==4)
(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
(Python)
from math import isqrt
from sympy import primepi, primerange, integer_nthroot
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

Crossrefs

Cf. A072000, A072114.

Partial sums of A101637.

Sequence in context: A342696 A064459 A279758 * A094382 A146167 A346622

Adjacent sequences: A082993 A082994 A082995 * A082997 A082998 A082999

Keyword

nonn,easy

Author

Benoit Cloitre, May 30 2003

Status

approved