%I #21 Feb 17 2023 22:34:25
%S 1,6,10,12,14,20,22,24,26,28,34,38,40,44,46,52,56,58,62,68,74,76,80,
%T 82,86,88,92,94,104,106,116,118,122,124,134,136,142,146,148,152,158,
%U 164,166,172,178,184,188,194,202,206,208,212,214,218,226,232,236,244,248
%N Numbers k such that A002322(k) = A023900(k).
%C Question: Does the multiplicity of any prime factor greater than 2 rise above the multiplicity of 2?
%C Answer: Yes, the first examples are 26617248, 117876384, 120115872, 124968096, 132433056, ... . - _Amiram Eldar_, Jan 20 2023
%t q[n_] := CarmichaelLambda[n] == Times @@ (1 - First[#]& /@ FactorInteger[n]); q[1] = True; Select[Range[250], q] (* _Amiram Eldar_, Jan 17 2023 *)
%o (Python)
%o from sympy import divisors, mobius, reduced_totient
%o def a002322(n): return reduced_totient(n)
%o def a023900(n): return sum([d*mobius(d) for d in divisors(n)])
%o print([k for k in range(1, 254) if a002322(k) == a023900(k)])
%o (PARI) isok(k) = lcm(znstar(k)[2]) == sumdivmult(k, d, d*moebius(d)); \\ _Michel Marcus_, Jan 20 2023
%Y Cf. A002322, A023900.
%K nonn
%O 1,2
%A _Torlach Rush_, Jan 16 2023