

A290805


Least Carmichael number whose Euler totient function value is an nth power.


1



561, 1729, 63973, 1729, 367939585, 63973, 294409, 232289960085001, 11570858964626401, 79939760257, 509033161, 611559276803883001, 13079177569, 27685385948423487745, 26979791457662785, 287290964059686145, 13046319747121261903830001, 7847507962539316696504321, 993942550111105, 6280552422566791778305, 24283361157780097, 759608966313690599499265, 6657107145346817668085761
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Banks proved that for each positive integer N there are an infinite number of Carmichael numbers whose Euler totient function value is an Nth power. Therefore this sequence is infinite.
The terms were calculated using Pinch's tables of Carmichael numbers (see link below).
a(25) = 33420122657338444417, a(26) = 239468866473584181889, and there are no more terms below 10^22.  Amiram Eldar, Apr 20 2024


LINKS



EXAMPLE

phi(1729) = 36^2 = 6^4 while phi(561) and phi(1105) are not perfect powers, therefore a(2) = a(4) = 1729.


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



