A377121 Numbers whose totient is refactorable.

1, 2, 3, 4, 6, 13, 15, 16, 19, 20, 21, 24, 26, 27, 28, 30, 35, 36, 37, 38, 39, 41, 42, 45, 52, 54, 55, 56, 57, 61, 63, 70, 72, 73, 74, 75, 76, 77, 78, 82, 84, 87, 88, 89, 90, 91, 93, 95, 97, 99, 100, 108, 109, 110, 111, 114, 115, 116, 117, 119, 122, 123, 124, 126, 129, 132, 133, 135, 137, 146, 147, 148, 150, 152, 153

Offset

1,2

Comments

If k is an odd term, 2*k is also a term due to the multiplicative nature of the totient function and their totients are equal.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

3, 4, and 6 are terms as their totients equal 2, which is the second refactorable number.

Maple

filter:= proc(n) local p;
  p:= numtheory:-phi(n);
  p mod numtheory:-tau(p) = 0
end proc:
select(filter, [$1..200]); # Robert Israel, Dec 12 2024

Mathematica

Select[Range[200], Mod[EulerPhi[#], DivisorSigma[0, EulerPhi[#]]]==0&]

Prog

(PARI) for(n=1, 200, a=eulerphi(n); a%numdiv(a)==0&&print1(n", "))
(Python)
from sympy import divisor_sigma, totient
for i in range(1, 200):
    if totient(i)%divisor_sigma(totient(i), 0)==0:
        print(i, end=", ")

Crossrefs

Cf. A000010, A033950.

Sequence in context: A018765 A274694 A352580 * A096988 A066463 A073146

Adjacent sequences: A377118 A377119 A377120 * A377122 A377123 A377124

Keyword

nonn

Author

Waldemar Puszkarz, Oct 17 2024

Status

approved