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A036386
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Number of prime powers (p^2, p^3,...) <= 2^n.
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6
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0, 1, 2, 4, 7, 9, 13, 16, 20, 26, 31, 40, 50, 61, 78, 93, 119, 150, 189, 242, 310, 400, 525, 684, 900, 1190, 1581, 2117, 2836, 3807, 5136, 6948, 9425, 12811, 17437, 23788, 32517, 44512, 60971, 83640, 114899, 157948, 217336, 299360, 412635, 569193
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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LINKS
| Index entries for sequences related to numbers of primes in various ranges
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FORMULA
| a(n)=Sum[Pi(Floor[2^( n/j )])], j=2, ...n+1] the summation starts with squares(j=2); for arbitrary range(=y) y^(1/j) argument has to be used.
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EXAMPLE
| The 9 prime-powers not exceeding 64 are 4, 8, 9, 16, 25, 27, 32, 49, 64.
n = 25, a(25) = 900 Pi(5792) + Pi(322) + Pi(76) + Pi(32) + Pi(17) + Pi(11) + Pi(8) + Pi(6) + Pi(5) + Pi(4) + Pi(4) + Pi(3) + Pi(3) + Pi(3) + Pi(2) + Pi(2) + Pi(2) + Pi(2) + Pi(2) + Pi(2) + Pi(2) + Pi(2) + Pi(2) + Pi(2) + Pi(1) = 760 + 66 + 21 + 11 + 7 + 5 + 4 + 3 + 3 + 2 + 2 + 2 + 2 + 2 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 0
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MATHEMATICA
| f[n_] := Length@ Union@ Flatten@ Table[ Prime[j]^k, {k, 2, n + 1}, {j, PrimePi[2^(n/k)]}]; Array[f, 46] (* Robert G. Wilson v, Jul 08 2011 *)
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CROSSREFS
| Cf. A007053, A029837, A036378-A036390.
Sequence in context: A129259 A077597 A183873 * A099847 A014817 A139444
Adjacent sequences: A036383 A036384 A036385 * A036387 A036388 A036389
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu)
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EXTENSIONS
| More terms from Labos E. (labos(AT)ana.sote.hu), May 07 2001
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