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

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

2,1

Links

Table of n, a(n) for n=2..50.

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.

Example

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

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 *)

Crossrefs

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

Sequence in context: A255470 A267710 A306896 * A341267 A219910 A334569

Adjacent sequences: A087233 A087234 A087235 * A087237 A087238 A087239

Keyword

nonn

Author

Labos Elemer, Sep 04 2003

Extensions

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

Status

approved