A350777 Numbers k where phi(k) divides k - 3.

1, 2, 3, 9, 195, 5187, 1141967133868035, 3658018932844533311864835

Offset: 1

Author

Albert Böschow and Dennis Gruhlke, Jan 15 2022

Keywords

• nonn
• more

Comments

Numbers in this sequence larger than 2 have to be odd, since phi(n) is even for n > 2, so n - 3 cannot be odd. Therefore n itself must be odd.

Terms having (k-3)/phi(k) = 2 are shared with A226105. - Max Alekseyev, Oct 26 2023

Examples

			phi(195) = 96, 195 - 3 = 192, and 96 divides 192.
		

Crossrefs

Cf. A000010, A007694, A226105.

Programs

Mathematica

Select[Range[6000], Divisible[#-3, EulerPhi[#]] &] (* Amiram Eldar, Jan 19 2022 *)

PARI

isok(k) = !((k-3) % eulerphi(k)); \\ Michel Marcus, Jan 19 2022

Python

from sympy import totient
print("1, 2", end=", ")
for k in range (3, 10**8, 2):
    if (k-3)%totient(k)==0:
        print(k, end=", ", flush=True) # Martin Ehrenstein, Mar 26 2022

Extensions

a(7)-a(8) from Max Alekseyev, Nov 05 2023