OFFSET
1,1
COMMENTS
Subsequence of A051270. 4620 = 2^2*3*5*7*11 is in A051270 but not in here, for example. - R. J. Mathar, Nov 10 2014
LINKS
T. D. Noe, Table of n, a(n) for n = 1..10000
EXAMPLE
a(1) = 2310 = 2 * 3 * 5 * 7 * 11 = A002110(5) = 5#.
a(2) = 2730 = 2 * 3 * 5 * 7 * 13.
a(3) = 3570 = 2 * 3 * 5 * 7 * 17.
a(10) = 6006 = 2 * 3 * 7 * 11 * 13.
MAPLE
A046387 := proc(n)
option remember;
local a;
if n = 1 then
2*3*5*7*11 ;
else
for a from procname(n-1)+1 do
if A001221(a)= 5 and issqrfree(a) then
return a;
end if;
end do:
end if;
end proc: # R. J. Mathar, Oct 13 2019
MATHEMATICA
f5Q[n_]:=Last/@FactorInteger[n]=={1, 1, 1, 1, 1}; lst={}; Do[If[f5Q[n], AppendTo[lst, n]], {n, 8!}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 26 2008 *)
PROG
(PARI) is(n)=factor(n)[, 2]==[1, 1, 1, 1, 1]~ \\ Charles R Greathouse IV, Sep 17 2015
(PARI) is(n)= omega(n)==5 && bigomega(n)==5 \\ Hugo Pfoertner, Dec 18 2018
(Python)
from math import isqrt, prod
from sympy import primerange, integer_nthroot, primepi
def A046387(n):
def g(x, a, b, c, m): yield from (((d, ) for d in enumerate(primerange(b+1, isqrt(x//c)+1), a+1)) if m==2 else (((a2, b2), )+d for a2, b2 in enumerate(primerange(b+1, integer_nthroot(x//c, m)[0]+1), a+1) for d in g(x, a2, b2, c*b2, m-1)))
def f(x): return int(n+x-sum(primepi(x//prod(c[1] for c in a))-a[-1][0] for a in g(x, 0, 1, 1, 5)))
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 30 2024
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Patrick De Geest, Jun 15 1998
EXTENSIONS
Entry revised by N. J. A. Sloane, Apr 10 2006
STATUS
approved