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 A038627 Number of solutions x to n * pi(x) = x, where pi(x) = number of primes <= x. 15

%I

%S 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

%N Number of solutions x to n * pi(x) = x, where pi(x) = number of primes <= x.

%C Equivalently, a(n) is number of solutions x to the equation pi(n*x) = x. - _Farideh Firoozbakht_, 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 because 15927 is the only solution of the equation pi(11*x) = x.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeCountingFunction.html">Prime Counting Function.</a>

%e 11*pi(x) = x has only 1 solution, so a(11) = 1.

%Y Cf. A038623-A038626, A102281, A087237.

%K nonn

%O 1,2

%A _Jud McCranie_

%E Vasiliy Danilov (danilovv(AT)usa.net) proved that solutions exist for each n>1.

%E One more term from Labos E. (labos(AT)ana.sote.hu), Sep 05 2003

%E a(24)-a(26) from Labos E. (labos(AT)ana.sote.hu), Sep 12 2003

%E Edited by _N. J. A. Sloane_, Sep 06 2008 at the suggestion of R. J. Mathar

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Last modified May 24 07:09 EDT 2013. Contains 225617 sequences.