OFFSET
1,1
COMMENTS
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
FORMULA
MATHEMATICA
Select[Range[150], Nor[PrimePowerQ[#], SquareFreeQ[#]] &]^2
PROG
(PARI) isok(k) = !issquarefree(k) && !isprimepower(k); \\ A126706
apply(sqr, select(isok, [1..200])) \\ Michel Marcus, Feb 07 2025
(Python)
from math import isqrt
from sympy import primepi, integer_nthroot, mobius
def A380857(n):
def bisection(f, kmin=0, kmax=1):
while f(kmax) > kmax: kmax <<= 1
kmin = kmax >> 1
while kmax-kmin > 1:
kmid = kmax+kmin>>1
if f(kmid) <= kmid:
kmax = kmid
else:
kmin = kmid
return kmax
def f(x): return int(n+sum(primepi(integer_nthroot(x, k)[0]) for k in range(2, x.bit_length()))+sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1)))
return bisection(f, n, n)**2 # Chai Wah Wu, Feb 08 2025
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michael De Vlieger, Feb 06 2025
STATUS
approved