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A290793 Carmichael numbers k such that Euler totient function of k (phi(k)) is a cube.

%I A290793 #25 Apr 22 2024 14:28:43
%S A290793 63973,18162001,26921089,133205761,225745345,490503601,496050841,
%T A290793 698548201,1031750401,1100674561,1384157161,2178944461,3805181281,
%U A290793 11351100241,12648201841,26498875681,26542598401,28553256865,28645206001,37590868801,39866123377,40527674881
%N A290793 Carmichael numbers k such that Euler totient function of k (phi(k)) is a cube.
%C A290793 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 A290793 The terms were calculated using Pinch's tables of Carmichael numbers (see link below).
%H A290793 Amiram Eldar, <a href="/A290793/b290793.txt">Table of n, a(n) for n = 1..10000</a> (calculated using data from Claude Goutier)
%H A290793 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 A290793 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 A290793 R. G. E. Pinch, <a href="http://s369624816.websitehome.co.uk/rgep/cartable.html">Tables relating to Carmichael numbers</a>.
%H A290793 <a href="/index/Ca#Carmichael">Index entries for sequences related to Carmichael numbers</a>.
%e A290793 phi(63973) = 36^3.
%t A290793 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 A290793 Intersection of A002997 (Carmichael numbers) and A039771.
%Y A290793 Cf. A000010, A000578, A272798.
%K A290793 nonn
%O A290793 1,1
%A A290793 _Amiram Eldar_, Aug 10 2017