cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Original entry on oeis.org

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

Views

Author

Labos Elemer, Sep 04 2003

Keywords

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.]

Examples

			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

Links

Crossrefs

Cf. A038623-A038627, A057809, A087235-A087240.
Cf. A102281.

Programs

  • 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 *)

Formula

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

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

A087241 Consecutive min and max-terms of solution-clusters of A057809, i,e, least and largest solutions to n=x/A000720[x].

Original entry on oeis.org

2, 8, 27, 33, 96, 120, 330, 360, 1008, 1134, 3059, 3094, 8408, 8472, 23526, 24300, 64540, 64720, 175197, 175197, 480852, 481452, 1304498, 1304719, 3523884, 3524654, 9557955, 9560100, 25874752, 25874784, 70115412, 70119985, 189961182, 189969354, 514272411, 514278263
Offset: 2

Views

Author

Labos Elemer, Sep 04 2003

Keywords

Links

Crossrefs

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

Extensions

More terms from Giovanni Resta, Sep 01 2018

A087236 a(n) is the difference between the largest and smallest integer solutions to n=x/pi(x), where pi(x) = A000720(x).

Original entry on oeis.org

6, 6, 24, 30, 126, 35, 64, 774, 180, 0, 600, 221, 770, 2145, 32, 4573, 8172, 5852, 5720, 7035, 792, 7774, 5256, 2825, 104, 2484, 1008, 2088, 8880, 9176, 10464, 759, 68, 5880, 23688, 28490, 3420, 49686, 58160, 62074, 136878, 26316, 264, 130320, 16882, 705, 96528, 14063, 95750
Offset: 2

Views

Author

Labos Elemer, Sep 04 2003

Keywords

Examples

			n=22: a(22) = 10246936436-10246935644 = 792 = 22*36.
a(2) = 6 since x/pi(x) = 2 for x = {2,4,6,8}; 8 - 2 = 6. - _Michael De Vlieger_, Mar 25 2017

Crossrefs

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

Programs

  • Mathematica
    Last@ # - First@ # & /@ 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 *)

Formula

a(n) = Max{x; n*pi(n)=x} - Min{x; n*pi(n)=x} = A038625(n) - A087235(n).
a(n) is divisible by n, the quotients are in A087237.

Extensions

a(27)-a(50) obtained from the values of A038625 computed by Jan Büthe. - Giovanni Resta, Sep 01 2018
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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