A379851 Numbers k such that phi(k) does not divide k. Complement of A007694.

3, 5, 7, 9, 10, 11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89

Offset: 1

Author

Franz Vrabec, Jan 04 2025

Keywords

• nonn

Comments

Let PHI(n) the set of all numbers x such there is a k-fold iteration of Euler's totient function phi = A000010 on x resulting in n. The numbers a(n) are exactly the numbers for which PHI(a(n)) is a finite set (possibly empty).

Contains A007617.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A007617. Complement of A007694.

Programs

Maple

filter:= n -> n mod numtheory:-phi(n) <> 0:
select(filter, [$1..100]); # Robert Israel, Feb 04 2025

Mathematica

Select[Range[100], ! Divisible[#, EulerPhi[#]] &] (* Amiram Eldar, Jan 08 2025 *)