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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, 4n 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=1, 18, print(sum(1, x=2, 4*n, -mu(x)*(floor(10^(n/x)-1))))

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 October 18 07:35 EDT 2019. Contains 328146 sequences. (Running on oeis4.)