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 N-th 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
William D. Banks, Carmichael Numbers with a Square Totient, Canadian Mathematical Bulletin, Vol. 52, No. 1 (2009), pp. 3-8.
Claude Goutier, Compressed text file carm10e22.gz containing all the Carmichael numbers up to 10^22.
R. G. E. Pinch, Tables relating to Carmichael numbers.
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
Amiram Eldar, Aug 11 2017
EXTENSIONS
a(1) prepended by David A. Corneth, Aug 11 2017
a(14)-a(16), a(19)-a(21) calculated using data from Claude Goutier and added by Amiram Eldar, Apr 20 2024
a(17)-a(18), a(22)-a(23) from Max Alekseyev, Apr 25 2024
STATUS
approved