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A129827
Numbers k such that Euler's totient phi(k) divided by 2 is a perfect square.
1
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
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
KEYWORD
nonn,changed
AUTHOR
Walter Nissen, May 20 2007
STATUS
approved