A333314 Composite non-Carmichael numbers k such that rad(phi(k)) divides k-1, where rad(k) is the squarefree kernel of k (A007947) and phi is the Euler totient function (A000010).

15, 51, 85, 91, 133, 247, 255, 259, 435, 451, 481, 511, 595, 679, 703, 763, 771, 949, 1111, 1141, 1261, 1285, 1351, 1387, 1417, 1615, 1695, 1843, 1891, 2047, 2071, 2091, 2119, 2431, 2509, 2701, 2761, 2955, 3031, 3097, 3145, 3277, 3367, 3409, 3589, 3655, 3667

Offset: 1

Author

Amiram Eldar, Mar 14 2020

Keywords

• nonn

Comments

McNew and Wright proved that this sequence is infinite.

Examples

			15 = 3 * 5 is a term since it is composite and not a Carmichael number, and rad(phi(15)) = rad(8) = 2 divides 15 - 1 = 14.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Nathan McNew and Thomas Wright, Infinitude of k-Lehmer numbers which are not Carmichael, International Journal of Number Theory, Vol. 12, No. 7 (2016), pp. 1863-1869; preprint, arXiv:1508.05547 [math.NT], 2015.

Crossrefs

Complement of the primes and Carmichael numbers (union of A000010 and A002997) with respect to A187731.

Complement of A002997 with respect to A238574.

Cf. A007947, A238575.

Programs

Mathematica

rad[n_] := Times @@ (First@# & /@ FactorInteger[n]); Select[Range[4000], Divisible[#-1, rad[EulerPhi[#]]] && !Divisible[#-1, CarmichaelLambda[#]] &]