OFFSET
1,2
COMMENTS
The larger endpoint is always twice the value of the smaller endpoint.
Conjecture 1: The number of solutions, excluding endpoints is always 0, or an odd number. (known to n = 2 * 10^5)
Conjecture 2: If both endpoints are divisible by 5, then the number of solutions (excluding terms of A007366) is of the form 4k + 1. (known to n = 2 * 10^5)
A007366 is contained in this sequence and the number of solutions, excluding endpoints is always 0.
Terms of this sequence are totients with a single odd totient inverse.
LINKS
Michel Marcus, Table of n, a(n) for n = 1..2441
Max Alekseyev, PARI scripts for various problems
EXAMPLE
2 is in the sequence because {phi^-1(2)} = {3,4,6}, and 2 = 6 / 3.
8 is in the sequence because {phi^-1(8)} = {15,...,30}, and 2 = 30 / 15.
10 is in the sequence because {phi^-1(10)} = {11,22}, and 2 = 22 / 11.
MATHEMATICA
With[{nn = 67}, Take[#, nn] &@ Keys@ Select[KeySort@ PositionIndex@ Array[EulerPhi, nn^2], IntegerQ[#2/#1] & @@ {First@ #, Last@ #} &]] (* Michael De Vlieger, Dec 31 2017 *)
PROG
(PARI) isok(n) = my(vx = invphi(n)); (#vx > 1) && ((vecmax(vx) % vecmin(vx)) == 0); \\ Michel Marcus, Jul 18 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Torlach Rush, Dec 30 2017
STATUS
approved