A070549 - OEIS

A070549

a(n) = Cardinality{ k in range 1 <= k <= n such that Moebius(k) = -1 }.

0, 1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 14, 15, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 19, 19, 20, 20, 20, 20, 20, 21, 22, 22, 22, 23, 24, 24, 25, 25, 25, 25, 25, 26

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OFFSET

1,3

COMMENTS

mu(k)=-1 if k is the product of an odd number of distinct primes. See A057627 for mu(k)=0.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

From Amiram Eldar, Oct 01 2023: (Start)

a(n) = (A013928(n+1) - A002321(n))/2.

a(n) = A013928(n+1) - A070548(n).

a(n) = A070548(n) - A002321(n).