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A065515
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Number of prime powers <= n.
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10
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1, 2, 3, 4, 5, 5, 6, 7, 8, 8, 9, 9, 10, 10, 10, 11, 12, 12, 13, 13, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 19, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 22, 22, 22, 22, 23, 23, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25, 26, 26, 27, 27, 27, 28, 28, 28, 29, 29, 29, 29, 30, 30, 31
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Equally, number of finite fields of order <= n. - Neven Juric, Feb 05 2010
a(n) > pi(n) = A000720(n).
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REFERENCES
| F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, Chapter 4.
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LINKS
| R. Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Prime Power
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FORMULA
| Partial sums of A010055. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 22 2009]
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EXAMPLE
| There are 9 prime powers <= 12: 1=2^0, 2, 3, 4=2^2, 5, 7, 8=2^3, 9=3^2 and 11, so a(12) = 9.
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MATHEMATICA
| a[n_] := 1 + Count[ Range[2, n], p_ /; Length[ FactorInteger[p]] == 1]; Table[a[n], {n, 1, 73}] (* From Jean-François Alcover, Oct 12 2011 *)
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PROG
| (Haskell)
a065515 n = length $ takeWhile (<= n) a000961_list
-- Reinhard Zumkeller, Apr 25 2011
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CROSSREFS
| Cf. A000040, A000961, A000720.
A025528(n) = a(n) - 1.
Cf. A139555. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 27 2010]
Sequence in context: A020892 A196165 A138366 * A070545 A091863 A163296
Adjacent sequences: A065512 A065513 A065514 * A065516 A065517 A065518
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KEYWORD
| nice,nonn
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 27 2001
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