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A070428
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Number of perfect powers (A001597) not exceeding 10^n.
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7
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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; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n)=~sqrt(10^n).
In the programs for this sequence, 4n can be replaced by the smaller floor(n*log(10)/log(2)) - T. D. Noe (noe(AT)sspectra.com), Nov 17 2006
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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.
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LINKS
| Robert G. Wilson v, Table of n, a(n) for n = 1..1000.. [From Robert G. Wilson v (rgwv(AT)rgwv.com), May 22 2009]
Eric Weisstein's World of Mathematics, Perfect Power
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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.
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MATHEMATICA
| Do[ Print[1 + Sum[ -MoebiusMu[x]*Floor[10^(n/x) - 1], {x, 2, 4n}]], {n, 0, 24}]
Table[1 - Sum[ MoebiusMu[x]*Floor[10^(n/x) - 1], {x, 2, n*Log[10]/Log[2]}], {n, 0, 24}] [From Robert G. Wilson v (rgwv(AT)rgwv.com), May 22 2009]
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PROG
| (PARI) for(n=1, 18, print(sum(1, x=2, 4*n, -mu(x)*(floor(10^(n/x)-1))))
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CROSSREFS
| Cf. A001597.
Cf. A089579, A089580 (number of perfect powers (not including 1) < 10^n).
Sequence in context: A149424 A097112 A077284 * A190214 A052529 A049222
Adjacent sequences: A070425 A070426 A070427 * A070429 A070430 A070431
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KEYWORD
| easy,nonn
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AUTHOR
| Donald S McDonald (don.mcdonald(AT)paradise.net.nz), May 15 2002
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EXTENSIONS
| More terms from Larry Reeves (larryr(AT)acm.org), Oct 03 2002
Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 11 2002
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