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

1,1

Comments

McNew and Wright proved that this sequence is infinite.

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.

Example

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.

Mathematica

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

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.

Sequence in context: A127643 A227129 A238574 * A238575 A020144 A339880

Adjacent sequences: A333311 A333312 A333313 * A333315 A333316 A333317

Keyword

nonn

Author

Amiram Eldar, Mar 14 2020

Status

approved