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

1,1

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

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000010, A000290, A090698 (subsequence).

Sequence in context: A346504 A063477 A168219 * A325179 A308533 A369735

Adjacent sequences: A129824 A129825 A129826 * A129828 A129829 A129830

Keyword

nonn

Author

Walter Nissen, May 20 2007

Status

approved