A359875 Numbers k such that A002322(k) = A023900(k).

1, 6, 10, 12, 14, 20, 22, 24, 26, 28, 34, 38, 40, 44, 46, 52, 56, 58, 62, 68, 74, 76, 80, 82, 86, 88, 92, 94, 104, 106, 116, 118, 122, 124, 134, 136, 142, 146, 148, 152, 158, 164, 166, 172, 178, 184, 188, 194, 202, 206, 208, 212, 214, 218, 226, 232, 236, 244, 248

Offset

1,2

Comments

Question: Does the multiplicity of any prime factor greater than 2 rise above the multiplicity of 2?

Answer: Yes, the first examples are 26617248, 117876384, 120115872, 124968096, 132433056, ... . - Amiram Eldar, Jan 20 2023

Links

Table of n, a(n) for n=1..59.

Mathematica

q[n_] := CarmichaelLambda[n] ==  Times @@ (1 - First[#]& /@ FactorInteger[n]); q[1] = True; Select[Range[250], q] (* Amiram Eldar, Jan 17 2023 *)

Prog

(Python)
from sympy import divisors, mobius, reduced_totient
def a002322(n): return reduced_totient(n)
def a023900(n): return sum([d*mobius(d) for d in divisors(n)])
print([k for k in range(1, 254) if a002322(k) == a023900(k)])
(PARI) isok(k) = lcm(znstar(k)[2]) == sumdivmult(k, d, d*moebius(d)); \\ Michel Marcus, Jan 20 2023

Crossrefs

Cf. A002322, A023900.

Sequence in context: A036348 A100368 A128691 * A028919 A325231 A134620

Adjacent sequences: A359872 A359873 A359874 * A359876 A359877 A359878

Keyword

nonn

Author

Torlach Rush, Jan 16 2023

Status

approved