OFFSET
2,1
COMMENTS
a(n) is the difference between the largest and smallest solutions to n = x/pi(x), divided by n, where pi(x) = A000720(x).
Equivalently, a(n) is the difference between largest solution and smallest natural solution of the equation pi(n*x) = x. - Farideh Firoozbakht, Jan 09 2005 [Max Alekseyev observes that this is trivially equivalent to the first definition.]
LINKS
Jan Büthe, Table of n, a(n) for n = 2..50
FORMULA
EXAMPLE
n=22: a(22) = (10246936436-10246935644)/22 = 792/22 = 36.
a(2) = 3 because 1, 2, 3 & 4 are all solutions of pi(2*x) = x and 4 - 1 = 3; a(11) = 0 because 15927 is the only solution of the equation pi(11*x) = x and 15927 - 15927 = 0. - Farideh Firoozbakht, Jan 09 2005
MATHEMATICA
MapIndexed[(Last@ #1 - First@ #1)/(First@ #2 + 1) &, Values@ Rest@ KeySort@ PositionIndex@ Table[n/PrimePi[n] /. k_ /; Not@ IntegerQ@ k -> 0, {n, 2, 10^6}]] (* Michael De Vlieger, Mar 25 2017, Version 10 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Sep 04 2003
EXTENSIONS
Edited by N. J. A. Sloane, Oct 28 2008 at the suggestion of R. J. Mathar
24 additional terms from Jan Büthe, Jan 16 2015
STATUS
approved