OFFSET
1,1
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..43
EXAMPLE
a(3) = 805 = 5*7*23.
PROG
(Python)
from itertools import count
from math import prod, isqrt
from sympy import primerange, integer_nthroot, primepi, primorial
def A106418(n):
if n == 1: return 83
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(sum(primepi(x//prod(c[1] for c in a))-a[-1][0] for a in g(x, 0, 1, 1, n)))
def bisection(f, kmin, kmax, mmin, mmax):
while kmax-kmin > 1:
kmid = kmax+kmin>>1
mmid = f(kmid)
if mmid > mmin:
kmax, mmax = kmid, mmid
else:
kmin, mmin = kmid, mmid
return kmax
for l in count(len(str(primorial(n)))-1):
kmin, kmax = 8*10**l-1, 9*10**l-1
mmin, mmax = f(kmin), f(kmax)
if mmax>mmin: return bisection(f, kmin, kmax, mmin, mmax) # Chai Wah Wu, Aug 31 2024
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Ray Chandler, May 02 2005
STATUS
approved