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 A070428 Number of perfect powers (A001597) not exceeding 10^n. 10
 1, 4, 13, 41, 125, 367, 1111, 3395, 10491, 32670, 102231, 320990, 1010196, 3184138, 10046921, 31723592, 100216745, 316694005, 1001003332, 3164437425, 10004650118, 31632790244, 100021566157, 316274216762, 1000100055684 (list; graph; refs; listen; history; text; internal format)
 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 CROSSREFS Cf. A001597. Cf. A089579, A089580 (number of perfect powers (not including 1) < 10^n). Sequence in context: A213496 A220926 A077284 * A320563 A268989 A190214 Adjacent sequences:  A070425 A070426 A070427 * A070429 A070430 A070431 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

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Last modified April 16 05:26 EDT 2021. Contains 343030 sequences. (Running on oeis4.)