A363896 - OEIS

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

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OFFSET

1,1

COMMENTS

No more terms less than 1.6*10^7.

LINKS

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.

KEYWORD

nonn,more

AUTHOR

STATUS

approved