OFFSET
0,2
LINKS
Chai Wah Wu, Table of n, a(n) for n = 0..16
FORMULA
a(n) = A001694(10^n).
Limit_{n->oo} a(n)/10^(2n) = (zeta(3)/zeta(3/2))^2 = 0.21172829478335...
PROG
(Python)
from math import isqrt
from sympy import mobius, integer_nthroot
def A376092(n):
def squarefreepi(n):
return int(sum(mobius(k)*(n//k**2) for k in range(1, isqrt(n)+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
m = 10**n
def f(x):
c, l = m+x, 0
j = isqrt(x)
while j>1:
k2 = integer_nthroot(x//j**2, 3)[0]+1
w = squarefreepi(k2-1)
c -= j*(w-l)
l, j = w, isqrt(x//k2**3)
c -= squarefreepi(integer_nthroot(x, 3)[0])-l
return c
return bisection(f, m, m)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Chai Wah Wu, Sep 09 2024
STATUS
approved