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Search: id:A161961
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| A161961 |
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Denominator of ratio in lowest terms of Pi(n^2)/(n*Pi(n)), where Pi(x) = A000720(x). |
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+0
2
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| 1, 3, 4, 5, 18, 28, 16, 18, 8, 11, 30, 2, 21, 15, 16, 119, 21, 19, 80, 168, 44, 23, 72, 75, 117, 81, 252, 145, 150, 341, 88, 363, 374, 77, 66, 148, 2, 39, 480, 533, 273, 602, 616, 35, 644, 15, 40, 35, 750, 85, 260, 848, 864, 440, 896, 912, 464, 1003, 1020, 366, 279, 126, 96, 585
(list; graph; listen)
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OFFSET
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2,2
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COMMENT
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Conjecture: S(n) = Pi(n^2)/(n*Pi(n)) ~ 1/2. The sequence is highly oscillatory but for 51000<n<51000, the ratio is already between 0.46 and 0.48.
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EXAMPLE
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The first few terms are: 1, 2/3, 3/4, 3/5, 11/18, 15/28, 9/16, 11/18, 5/8,...
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MAPLE
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A000720 := proc(n) numtheory[pi](n) ; end:
A161961 := proc(n) A000720(n^2)/n/A000720(n) ; denom(%) ; end: seq(A161961(n), n=2..120) ; # R. J. Mathar, Oct 05 2009
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MATHEMATICA
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Table[PrimePi[n^2]/(n*PrimePi[n]), {n, 1, 100}]
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CROSSREFS
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Cf. A161960, A000720.
Sequence in context: A051033 A031199 A059184 this_sequence A161474 A084930 A114336
Adjacent sequences: A161958 A161959 A161960 this_sequence A161962 A161963 A161964
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KEYWORD
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nonn,frac
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AUTHOR
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Daniel Tisdale (daniel6874(AT)gmail.com), Jun 22 2009
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EXTENSIONS
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Keyword:frac added by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 30 2009
Definition corrected and sequence extended - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 05 2009
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