OFFSET
1,1
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
FORMULA
Product p_i^e_i with Sum e_i >= 7.
MATHEMATICA
Select[Range[2000], PrimeOmega[#]>6&] (* Harvey P. Dale, Nov 16 2012 *)
PROG
(PARI) is(n)=bigomega(n)>6 \\ Charles R Greathouse IV, Sep 17 2015
(Python)
from math import prod, isqrt
from sympy import primerange, integer_nthroot, primepi
def A046307(n):
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)))
def f(x): return int(n+primepi(x)+sum(sum(primepi(x//prod(c[1] for c in a))-a[-1][0] for a in g(x, 0, 1, 1, i)) for i in range(2, 7)))
kmin, kmax = 1, 2
while f(kmax) >= kmax:
kmax <<= 1
while True:
kmid = kmax+kmin>>1
if f(kmid) < kmid:
kmax = kmid
else:
kmin = kmid
if kmax-kmin <= 1:
break
return kmax # Chai Wah Wu, Aug 23 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Patrick De Geest, Jun 15 1998
STATUS
approved