A363896 - OEIS

%I #51 Aug 07 2023 14:54:10

%S 9,15,16,42

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

%C No more terms less than 1.6*10^7.

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

%t Select[Range[2, 1000], EulerPhi[#] == Plus @@ Times @@@ FactorInteger[#] &] (* _Amiram Eldar_, Jun 27 2023 *)

%o (Python)

%o from sympy import factorint,totient

%o A001414 = lambda k: sum(p*e for p, e in factorint(k).items())

%o def g():

%o   k = 2

%o   while True:

%o     if A001414(k) == totient(k): yield(k)

%o     k += 1

%o for a_n in g():

%o   print(a_n)

%o (PARI) is(k) = my(f=factor(k)); f[, 1]~*f[, 2] == eulerphi(f); \\ _Amiram Eldar_, Jun 27 2023

%Y Subsequence of A257048.

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

%K nonn,more

%O 1,1

%A _Darío Clavijo_, Jun 26 2023