OFFSET
1,2
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Prime Power
Eric Weisstein's World of Mathematics, Squarefree
EXAMPLE
42 is in the sequence because 42 = 2*3*7 (3 distinct prime factors).
81 is in the sequence because 81 = 3^4 (4 prime factors, 1 distinct).
MATHEMATICA
Select[Range[110], PrimePowerQ[#] || SquareFreeQ[#] &]
Select[Range[110], PrimeNu[#] == 1 || PrimeNu[#] == PrimeOmega[#] &]
PROG
(Python)
from math import isqrt
from sympy import primepi, integer_nthroot, mobius
def A303554(n):
def f(x): return int(n+x-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)))
m, k = n, f(n)
while m != k:
m, k = k, f(k)
return m # Chai Wah Wu, Aug 19 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 26 2018
STATUS
approved