OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
PROG
(PARI)
ispowerful(n)={local(h); if(n==1, h=1, h=(vecmin(factor(n)[, 2])>1)); return(h)}
proxpowerful(n)={local(k); k=n+1; while(!ispowerful(k), k+=1); return(k)}
{for(i=1, 5000, if(ispowerful(i), m=proxpowerful(i); p=primepi(m)-primepi(i); print1(p, ", ")))}
(Python)
from math import isqrt
from sympy import mobius, integer_nthroot, primepi
def A240590(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
def f(x):
c, l = n+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 -primepi(a:=bisection(f, n, n))+primepi(bisection(lambda x:f(x)+1, a, a)) # Chai Wah Wu, Sep 15 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Antonio Roldán, Apr 08 2014
STATUS
approved