A072778 Number of powers of squarefree numbers <= n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14, 15, 16, 16, 17, 17, 18, 19, 20, 20, 21, 22, 23, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 34, 35, 36, 37, 37, 37, 38, 39, 39, 40, 40, 41, 41, 42, 42, 43, 43, 44, 45, 46, 46, 47, 48, 48, 49, 50, 51, 52, 52, 53, 54, 55, 55

Offset: 1

Author

Reinhard Zumkeller, Jul 10 2002

Keywords

• nonn

Crossrefs

Cf. A072774, A013928.

Programs

Python

from math import isqrt
from sympy import mobius, integer_nthroot
def A072778(n):
    def f(x): return int(sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1)))
    return 2-(m:=n.bit_length())+sum(f(integer_nthroot(n,k)[0]) for k in range(1,m)) # Chai Wah Wu, Aug 19 2024