|
|
A281016
|
|
Numbers n such that n, phi(n) and cototient(n) are all perfect powers.
|
|
1
|
|
|
8, 16, 32, 64, 125, 128, 256, 512, 1024, 2048, 3125, 4096, 4913, 8192, 16384, 32768, 50653, 65536, 78125, 131072, 262144, 524288, 1030301, 1048576, 1419857, 1953125, 2097152, 4194304, 7645373, 8388608, 16777216, 16974593, 33554432, 35831808, 48828125, 64481201, 67108864, 69343957
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
This sequence does not contain only prime powers. Least term that has a prime factor which is not of the form m^2 + 1 is 35831808 = 2^14 * 3^7. The next one is 102503232 = 2^6 * 3^6 * 13^3. There are infinitely many such numbers.
|
|
LINKS
|
|
|
EXAMPLE
|
125 = 5^3 is a term because phi(5^3) = 10^2 and cototient(5^3) = 5^2.
|
|
MATHEMATICA
|
Select[Range[10^6], Times @@ Boole@ Map[Or[# == 1, GCD @@ FactorInteger[#][[All, 2]] > 1] &, {#, EulerPhi@ #, # - EulerPhi@ #}] > 0 &] (* Michael De Vlieger, Jan 14 2017 *)
|
|
PROG
|
(PARI) is(n) = ispower(eulerphi(n)) && ispower(n-eulerphi(n)) && ispower(n);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|