OFFSET
0,2
COMMENTS
In the programs for this sequence, 4*n can be replaced by the smaller floor(n*log(10)/log(2)). - T. D. Noe, Nov 17 2006
REFERENCES
The Dominion (Wellington, NZ), 'wtd sell', 9 Nov. 1991.
sci.math, powers not exceeding n. nz science monthly advt, March 1993, 1:80 integers 1..10000 is perfect square or higher power.
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 0..999
Eric Weisstein's World of Mathematics, Perfect Power
FORMULA
a(n) ~ sqrt(10^n).
EXAMPLE
a(1) = 4 because the powers 1, 4, 8, 9 do not exceed 10^1.
a(2) = 13 because 1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 81 & 100, are the only perfect power numbers less than or equal to 100.
MATHEMATICA
f[n_] := 1 - Sum[ MoebiusMu[x]*Floor[10^(n/x) - 1], {x, 2, n*Log2[10]}]; Array[f, 25, 0] (* Robert G. Wilson v, May 22 2009; modified Aug 04 2014 *)
PROG
(PARI) for(n=0, 25, print1(sum(x=2, 4*n, -moebius(x)*(floor(10^(n/x)-1)))+1, ", ")); \\ Slightly modified by Jinyuan Wang, Mar 02 2020
(Python)
from sympy import mobius, integer_nthroot
def A070428(n): return int(1-sum(mobius(x)*(integer_nthroot(10**n, x)[0]-1) for x in range(2, (10**n).bit_length()))) # Chai Wah Wu, Aug 13 2024
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Donald S. McDonald, May 15 2002
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), Oct 03 2002
Edited and extended by Robert G. Wilson v, Oct 11 2002
STATUS
approved