A069043 Composite numbers k with no prime factor among (2, 3) (cf. A038509) and such that phi(k) < 2*k/3.

385, 455, 595, 665, 805, 1015, 1085, 1925, 2275, 2695, 2975, 3185, 3325, 4025, 4165, 4235, 4655, 5005, 5075, 5425, 5635, 5915, 6545, 7105, 7315, 7595, 7735, 8645, 8855, 9625, 10115, 10465, 11165, 11305, 11375, 11935, 12155, 12635, 13195, 13475

Offset: 1

Author

Benoit Cloitre, Apr 03 2002

Keywords

• easy
• nonn

Comments

Almost all composite numbers k such that phi(k) > 2k/3 have no prime factor among 2 and 3.

Links

• Marius A. Burtea, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A038509, A067793.

Programs

Magma

[k:k in [1..14000]| not IsPrime(k) and Gcd(6,k) eq 1 and EulerPhi(k) lt 2*k/3]; // Marius A. Burtea, Oct 01 2019

Mathematica

Select[Flatten @ Table[6*n + {1, 5}, {n, 0, 2500}], CompositeQ[#] && EulerPhi[#] < 2*#/3 &] (* Amiram Eldar, Jun 09 2022 *)

PARI

lista(nn) = {forcomposite(n=1, nn, if ((gcd(n, 6) == 1) && (n/eulerphi(n) > 3/2), print1(n, ", ")););} \\ Michel Marcus, Jul 05 2015

Formula

A038509 SETMINUS A067793: numbers in A038509 but not in A067793.