OFFSET
1,1
COMMENTS
A squarefree subsequence of A033993. Numbers like 420 = 2^2*3*5*7 with at least one prime exponent greater than 1 in the prime signature are excluded here. - R. J. Mathar, Apr 03 2011
Numbers such that omega(n) = bigomega(n) = 4. - Michel Marcus, Dec 15 2015
LINKS
T. D. Noe, Table of n, a(n) for n = 1..10000
FORMULA
Intersection of A014613 (product of 4 primes) and A033993 (divisible by 4 distinct primes). - M. F. Hasler, Mar 24 2022
EXAMPLE
210 = 2*3*5*7;
330 = 2*3*5*11;
390 = 2*3*5*13;
462 = 2*3*7*11.
MATHEMATICA
fQ[n_] := Last /@ FactorInteger[n] == {1, 1, 1, 1}; Select[ Range[2000], fQ[ # ] &] (* Robert G. Wilson v, Aug 04 2005 *)
PROG
(PARI) is(n)=factor(n)[, 2]==[1, 1, 1, 1]~ \\ Charles R Greathouse IV, Sep 17 2015
(PARI) is(n) = omega(n)==4 && bigomega(n)==4 \\ Hugo Pfoertner, Dec 18 2018
(Python)
from math import isqrt
from sympy import primepi, primerange, integer_nthroot
def A046386(n):
def f(x): return int(n+x-sum(primepi(x//(k*m*r))-c for a, k in enumerate(primerange(integer_nthroot(x, 4)[0]+1), 1) for b, m in enumerate(primerange(k+1, integer_nthroot(x//k, 3)[0]+1), a+1) for c, r in enumerate(primerange(m+1, isqrt(x//(k*m))+1), b+1)))
def bisection(f, kmin=0, kmax=1):
while f(kmax) > kmax: kmax <<= 1
while kmax-kmin > 1:
kmid = kmax+kmin>>1
if f(kmid) <= kmid:
kmax = kmid
else:
kmin = kmid
return kmax
return bisection(f) # Chai Wah Wu, Aug 29 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Patrick De Geest, Jun 15 1998
STATUS
approved