

A038627


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


16



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, 15, 9, 15, 26, 22, 24, 9, 3, 14, 55, 36, 3, 65, 52, 33, 139, 42, 2, 85, 25, 7, 96, 16, 33
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OFFSET

1,2


COMMENTS

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.]
S. W. Golomb proved that a(n) > 0 for each integer n > 1.  Carlo Sanna, Nov 09 2015


LINKS

Table of n, a(n) for n=1..50.
S. W. Golomb, On the ratio of N to π(N), The American Mathematical Monthly, Vol. 69, No. 1 (Jan 1962), pp. 3637.
Robert T. Harger and William L. Hightower, An Interesting Property of x/π(x), The College Mathematics Journal Vol. 40, No. 3 (May 2009), pp. 213214.
Eric Weisstein's World of Mathematics, Prime Counting Function.


EXAMPLE

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


CROSSREFS

Cf. A038623, A038624, A038625, A038626, A102281, A087237.
Sequence in context: A238376 A237197 A006994 * A155835 A138187 A105342
Adjacent sequences: A038624 A038625 A038626 * A038628 A038629 A038630


KEYWORD

nonn,more


AUTHOR

Jud McCranie


EXTENSIONS

One more term from Labos Elemer, Sep 05 2003
a(24)a(26) from Labos Elemer, Sep 12 2003
Edited by N. J. A. Sloane, Sep 06 2008 at the suggestion of R. J. Mathar
a(27)a(29) from David Radcliffe, Sep 10 2014
a(29) corrected and a(30)a(50) obtained from the A038625 values computed by Jan Büthe.  Giovanni Resta, Aug 31 2018


STATUS

approved



