A290793 - OEIS

%I #25 Apr 22 2024 14:28:43

%S 63973,18162001,26921089,133205761,225745345,490503601,496050841,

%T 698548201,1031750401,1100674561,1384157161,2178944461,3805181281,

%U 11351100241,12648201841,26498875681,26542598401,28553256865,28645206001,37590868801,39866123377,40527674881

%N Carmichael numbers k such that Euler totient function of k (phi(k)) is a cube.

%C 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.

%C The terms were calculated using Pinch's tables of Carmichael numbers (see link below).

%H Amiram Eldar, <a href="/A290793/b290793.txt">Table of n, a(n) for n = 1..10000</a> (calculated using data from Claude Goutier)

%H William D. Banks, <a href="http://dx.doi.org/10.4153/CMB-2009-001-7">Carmichael Numbers with a Square Totient</a>, Canadian Mathematical Bulletin, Vol. 52, No. 1 (2009), pp. 3-8.

%H Claude Goutier, <a href="http://www-labs.iro.umontreal.ca/~goutier/OEIS/A055553/">Compressed text file carm10e22.gz containing all the Carmichael numbers up to 10^22</a>.

%H R. G. E. Pinch, <a href="http://s369624816.websitehome.co.uk/rgep/cartable.html">Tables relating to Carmichael numbers</a>.

%H <a href="/index/Ca#Carmichael">Index entries for sequences related to Carmichael numbers</a>.

%e phi(63973) = 36^3.

%t With[{s = Import["b002997.txt", "Data"][[All, -1]]}, Select[s, IntegerQ@ Power[EulerPhi@ #, 1/3] &]] (* _Michael De Vlieger_, Aug 14 2017, using b-file at A002997 *)

%Y Intersection of A002997 (Carmichael numbers) and A039771.

%Y Cf. A000010, A000578, A272798.

%K nonn

%O 1,1

%A _Amiram Eldar_, Aug 10 2017