A385822 Numbers k such that phi(k) is not a perfect square.

3, 4, 6, 7, 9, 11, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 35, 36, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 58, 59, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 77, 78, 79, 80, 81, 82, 83, 84, 86, 87, 88, 89

Offset

1,1

Links

Table of n, a(n) for n=1..71.

Example

Since phi(35) = 24 and there is no integer n such that n^2 = 24.

Mathematica

Select[Range[100], !IntegerQ[Sqrt[EulerPhi[#]]] &] (* Amiram Eldar, Aug 18 2025 *)

Prog

(Python)
from math import isqrt
from sympy import totient as phi
def ok(n): return isqrt(p:=phi(n))**2 != p
print([k for k in range(1, 110) if ok(k)]) # Michael S. Branicky, Aug 17 2025
(PARI) isok(k) = !issquare(eulerphi(k)); \\ Michel Marcus, Aug 18 2025

Crossrefs

Cf. A000010. Complement of A039770.

Sequence in context: A047516 A247425 A236444 * A286809 A352178 A244239

Adjacent sequences: A385819 A385820 A385821 * A385823 A385824 A385825

Keyword

nonn,easy

Author

Aidan Chen, Aug 11 2025

Status

approved