login
This site is supported by donations to The OEIS Foundation.

 

Logo

The OEIS is looking to hire part-time people to help edit core sequences, upload scanned documents, process citations, fix broken links, etc. - Neil Sloane, njasloane@gmail.com

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A071172 Number of squarefree integers <= 10^n. 15
1, 7, 61, 608, 6083, 60794, 607926, 6079291, 60792694, 607927124, 6079270942, 60792710280, 607927102274, 6079271018294, 60792710185947, 607927101854103, 6079271018540405, 60792710185403794 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The limit of a(n)/10^n is 6/Pi^2 (see A059956). [Gerard P. Michon, Apr 30 2009]

LINKS

J. Pawlewicz, Table of n, a(n) for n = 0..36

W. Hürlimann, A First Digit Theorem for Square-Free Integer Powers, Pure Mathematical Sciences, Vol. 3, 2014, no. 3, 129 - 139 HIKARI Ltd.

G. P. Michon, On the number of squarefree integers not exceeding N. [From Gerard P. Michon, Apr 30 2009]

J. Pawlewicz, Counting square-free numbers, arXiv preprint arXiv:1107.4890, 2011

Eric Weisstein's World of Mathematics, Squarefree

FORMULA

a(n) = Sum from i = 1 to 10^(n/2) of A008683(i)*floor(10^n/j^2). [Gerard P. Michon, Apr 30 2009]

MATHEMATICA

f[n_] := Sum[ MoebiusMu[i]Floor[n/i^2], {i, Sqrt@ n}]; Table[ f[10^n], {n, 0, 14}] (* Robert G. Wilson v, Aug 04 2012 *)

PROG

(PARI) a(n)=sum(d=1, sqrtint(n=10^n), moebius(d)*n\d^2) \\ Charles R Greathouse IV, Nov 14 2012

CROSSREFS

Cf. A005117, A053462.

Apart from initial term, same as A053462.

Binary counterpart is A143658. [Gerard P. Michon, Apr 30 2009]

Sequence in context: A113718 A177132 A077642 * A259335 A127688 A111532

Adjacent sequences:  A071169 A071170 A071171 * A071173 A071174 A071175

KEYWORD

nonn,changed

AUTHOR

Robert G. Wilson v, Jun 10 2002

EXTENSIONS

Extended by Eric W. Weisstein, Sep 14, 2003

3 more terms from Jud McCranie, Sep 01 2005

4 more terms from Gerard P. Michon, Apr 30 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified May 28 17:57 EDT 2017. Contains 287241 sequences.