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Search: id:A038627
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| A038627 |
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Number of solutions x to n * pi(x) = x, where pi(x) = number of primes <= x. |
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+0
16
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| 0, 4, 3, 3, 6, 7, 6, 6, 3, 9, 1, 18, 11, 12, 21, 3, 10, 33, 31, 32, 24, 8, 13, 32, 35, 4
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Equivalently, a(n) is number of solutions x to the equation pi(n*x) = x. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Jan 09 2005. For example, a(2) = 4 because 1, 2, 3 & 4 are all solutions of pi(2*x) = x and a(11) = 1 beacuse 15927 is the only solution of the equation pi(11*x) = x.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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EXAMPLE
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11*pi(x) = x has only 1 solution, so a(11)=1
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CROSSREFS
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Cf. A038623-A038626, A102281, A087237.
Sequence in context: A154913 A154915 A006994 this_sequence A155835 A138187 A055525
Adjacent sequences: A038624 A038625 A038626 this_sequence A038628 A038629 A038630
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KEYWORD
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nonn
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AUTHOR
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Jud McCranie (j.mccranie(AT)comcast.net)
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EXTENSIONS
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Vasiliy Danilov (danilovv(AT)usa.net) proved that solutions exist for each n>1.
One more term from Labos E. (labos(AT)ana.sote.hu), Sep 05 2003
a[24]=32, a[25]=35, a[26]=4 from Labos E. (labos(AT)ana.sote.hu), Sep 12 2003
Edited by N. J. A. Sloane (njas(AT)research.att.com), Sep 06 2008 at the suggestion of R. J. Mathar
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