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

1,4

Links

Table of n, a(n) for n=1..66.

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

Example

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

Prog

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

Crossrefs

Cf. A005117, A013928, A144338.

Sequence in context: A361674 A054633 A327982 * A242493 A261345 A243285

Adjacent sequences: A072487 A072488 A072489 * A072491 A072492 A072493

Keyword

nonn

Author

Amarnath Murthy, Jul 14 2002

Extensions

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

Status

approved