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. - Gerard P. Michon, Apr 30 2009
J. Pawlewicz, Counting square-free numbers, arXiv preprint arXiv:1107.4890 [math.NT], 2011.
Eric Weisstein's World of Mathematics, Squarefree
FORMULA
a(n) = Sum_{i=1..10^(n/2)} A008683(i)*floor(10^n/i^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
(PARI) a(n)=my(s); forsquarefree(d=1, sqrtint(n=10^n), s += n\d[1]^2 * moebius(d)); s \\ Charles R Greathouse IV, Jan 08 2018
(Python)
from math import isqrt
from sympy import mobius
def A071172(n): return sum(mobius(k)*(10**n//k**2) for k in range(1, isqrt(10**n)+1)) # Chai Wah Wu, May 10 2024
CROSSREFS
KEYWORD
nonn
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