A363896 Numbers k such that the sum of primes dividing k (with repetition) is equal to Euler's totient function of k.

9, 15, 16, 42

Offset

1,1

Comments

No more terms less than 1.6*10^7.

Links

Table of n, a(n) for n=1..4.

Formula

{k : A001414(k) = A000010(k)}.

Mathematica

Select[Range[2, 1000], EulerPhi[#] == Plus @@ Times @@@ FactorInteger[#] &] (* Amiram Eldar, Jun 27 2023 *)

Prog

(Python)
from sympy import factorint, totient
A001414 = lambda k: sum(p*e for p, e in factorint(k).items())
def g():
  k = 2
  while True:
    if A001414(k) == totient(k): yield(k)
    k += 1
for a_n in g():
  print(a_n)
(PARI) is(k) = my(f=factor(k)); f[, 1]~*f[, 2] == eulerphi(f); \\ Amiram Eldar, Jun 27 2023

Crossrefs

Subsequence of A257048.

Other sequences requiring a specific relationship between A000010(k) and A001414(k): A173327, A237798, A280936.

Sequence in context: A324879 A066942 A257048 * A061838 A037002 A071149

Adjacent sequences: A363893 A363894 A363895 * A363897 A363898 A363899

Keyword

nonn,more

Author

Darío Clavijo, Jun 26 2023

Status

approved