OFFSET
1,7
COMMENTS
Race between the number of squarefree numbers and round(n/zeta(2)).
First term < 0: a(172) = -1.
REFERENCES
G. H. Hardy and S. Ramanujan, The normal number of prime factors of a number n, Q. J. Math., 48 (1917), pp. 76-92.
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Fifth edition, Clarendon Press, 1979, pp. 269-270.
LINKS
Daniel Forgues, Table of n, a(n) for n=1..100000
Andrew Granville, ABC allows us to count squarefrees, International Mathematics Research Notices, Vol. 1998, No. 19 (1998), pp. 991-1109; alternative link.
FORMULA
MATHEMATICA
seq[lim_] := Accumulate[Boole[SquareFreeQ /@ Range[lim]]] - Round[Range[lim]/Zeta[2]]; seq[105] (* Amiram Eldar, Jan 20 2025 *)
CROSSREFS
Cf. A008966 (1 if n is squarefree, else 0).
Cf. A013928 (number of squarefree numbers < n).
Cf. A100112 (if n is the k-th squarefree number then k else 0).
Cf. A057627 (number of nonsquarefree numbers not exceeding n).
Cf. A005117 (squarefree numbers).
Cf. A013929 (nonsquarefree numbers).
Cf. A013661 (zeta(2)).
KEYWORD
sign
AUTHOR
Daniel Forgues, Mar 27 2009
STATUS
approved