A072490 Number of squarefree numbers (excluding 1) less than n.

0, 0, 1, 2, 2, 3, 4, 5, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 11, 12, 12, 13, 14, 15, 15, 15, 16, 16, 16, 17, 18, 19, 19, 20, 21, 22, 22, 23, 24, 25, 25, 26, 27, 28, 28, 28, 29, 30, 30, 30, 30, 31, 31, 32, 32, 33, 33, 34, 35, 36, 36, 37, 38, 38, 38, 39

Offset: 1

Author

Amarnath Murthy, Jul 14 2002

Keywords

• nonn

Examples

			a(10) = 5 as the squarefree numbers less than 10 are 2,3,5,6 and 7.
		

Crossrefs

Cf. A005117, A013928, A144338.

Programs

PARI

a(n) = sum(k=2, n-1, issquarefree(k)); \\ Michel Marcus, Sep 15 2019

Python

from math import isqrt
from sympy import mobius
def A072490(n): return int(sum(mobius(k)*((n-1)//k**2) for k in range(1, isqrt(n-1)+1)))-1 if n>1 else 0 # Chai Wah Wu, Aug 19 2024

Formula

a(n) = A013928(n) - 1, n > 1.

G.f.: (x/(1 - x)) * Sum_{k>=2} mu(k)^2*x^k. - Ilya Gutkovskiy, Sep 14 2019

Extensions

Name clarified and more terms from Ilya Gutkovskiy, Sep 14 2019