A129827 Numbers k such that Euler's totient phi(k) divided by 2 is a perfect square.

3, 4, 6, 15, 16, 19, 20, 24, 27, 30, 38, 51, 54, 64, 68, 73, 80, 91, 95, 96, 102, 111, 117, 120, 135, 146, 148, 152, 163, 182, 190, 216, 222, 228, 234, 243, 252, 255, 256, 270, 272, 275, 303, 320, 323, 326, 340, 365, 375, 384, 404, 408, 455, 459, 480, 486, 500

Offset: 1

Author

Walter Nissen, May 20 2007

Keywords

• nonn

Comments

Primes in this sequence are of the form 2*m^2+1 (see A090698). - Bernard Schott, Mar 07 2020

If k is an odd term, so is 2*k. If k is an even term, so is 4*k. - Waldemar Puszkarz, Oct 15 2024

Examples

			a(4) is 15 because phi(15) = 8, which is twice the square of 2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A000290, A090698 (subsequence).

Programs

Mathematica

Select[Range[500], IntegerQ @ Sqrt[EulerPhi[#]/2] &] (* Amiram Eldar, Mar 07 2020 *)

PARI

isok(n) = issquare(eulerphi(n)/2) \\ Michel Marcus, Jul 23 2013

Python

from sympy import totient
from sympy.ntheory.primetest import is_square
for i in range(3, 501):
    if is_square(int(totient(i)/2)):
        print(i, end=", ") # Waldemar Puszkarz, Oct 15 2024