OFFSET
1,1
LINKS
John Cerkan, Table of n, a(n) for n = 1..10000
FORMULA
Product p_i^e_i with Sum e_i >= 6.
a(n) = n + O(n (log log n)^4/log n). - Charles R Greathouse IV, Apr 07 2017
MATHEMATICA
Select[Range[1000], Total[Transpose[FactorInteger[#]][[2]]]>5&] (* Harvey P. Dale, Jan 13 2011 *)
Select[Range[1000], PrimeOmega[#]>5&] (* Harvey P. Dale, Apr 14 2019 *)
PROG
(PARI) is(n)=bigomega(n)>5 \\ Charles R Greathouse IV, Sep 17 2015
(Python)
from math import prod, isqrt
from sympy import primerange, primepi, integer_nthroot
def A046305(n):
def bisection(f, kmin=0, kmax=1):
while f(kmax) > kmax: kmax <<= 1
kmin = kmax >> 1
while kmax-kmin > 1:
kmid = kmax+kmin>>1
if f(kmid) <= kmid:
kmax = kmid
else:
kmin = kmid
return kmax
def almostprimepi(n, k):
if k==0: return int(n>=1)
def g(x, a, b, c, m): yield from (((d, ) for d in enumerate(primerange(b, isqrt(x//c)+1), a)) if m==2 else (((a2, b2), )+d for a2, b2 in enumerate(primerange(b, integer_nthroot(x//c, m)[0]+1), a) for d in g(x, a2, b2, c*b2, m-1)))
return int(sum(primepi(n//prod(c[1] for c in a))-a[-1][0] for a in g(n, 0, 1, 1, k)) if k>1 else primepi(n))
def f(x): return n+1+sum(almostprimepi(x, k) for k in range(1, 6))
return bisection(f, n, n) # Chai Wah Wu, Mar 29 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Patrick De Geest, Jun 15 1998
EXTENSIONS
Offset corrected by Andrew Howroyd, Aug 13 2024
STATUS
approved
