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

63973, 18162001, 26921089, 133205761, 225745345, 490503601, 496050841, 698548201, 1031750401, 1100674561, 1384157161, 2178944461, 3805181281, 11351100241, 12648201841, 26498875681, 26542598401, 28553256865, 28645206001, 37590868801, 39866123377, 40527674881

Offset: 1

Author

Amiram Eldar, Aug 10 2017

Keywords

• nonn

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).

Examples

			phi(63973) = 36^3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (calculated using data from Claude Goutier)
• 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.
• Index entries for sequences related to Carmichael numbers.

Crossrefs

Intersection of A002997 (Carmichael numbers) and A039771.

Cf. A000010, A000578, A272798.

Programs

Mathematica

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 *)