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

1,1

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

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 *)

Prog

(Python)
from sympy import integer_log
def A379851(n):
    def f(x): return n-(m:=integer_log(x, 3)[0])+sum((x//3**i).bit_length() for i in range(m+1))
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Jun 08 2026

Crossrefs

Cf. A000010, A007617. Complement of A007694.

Sequence in context: A369361 A326980 A281005 * A080259 A384011 A067715

Adjacent sequences: A379848 A379849 A379850 * A379852 A379853 A379854

Keyword

nonn,changed

Author

Franz Vrabec, Jan 04 2025

Status

approved