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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 (list; graph; refs; listen; history; text; internal format)
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. 36-37.

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. 213-214.

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

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Last modified January 28 00:31 EST 2020. Contains 331313 sequences. (Running on oeis4.)