A087237 a(n) = (Max{x : n*pi(x) = x} - Min{x : n*pi(x) = x})/n = A087236(n)/n.

3, 2, 6, 6, 21, 5, 8, 86, 18, 0, 50, 17, 55, 143, 2, 269, 454, 308, 286, 335, 36, 338, 219, 113, 4, 92, 36, 72, 296, 296, 327, 23, 2, 168, 658, 770, 90, 1274, 1454, 1514, 3259, 612, 6, 2896, 367, 15, 2011, 287, 1915

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

a(n) = A102281(n) - A038626(n). - Farideh Firoozbakht, Jan 09 2005

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

Cf. A038623-A038627, A057809, A087235-A087240.

Cf. A102281.

Sequence in context: A309512 A225367 A283479 * A275630 A102004 A233208

Adjacent sequences: A087234 A087235 A087236 * A087238 A087239 A087240

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