A356433 - OEIS

%I #28 Feb 02 2023 04:25:33

%S 1,4,27,72,108,192,576,800,1458,1728,2916,3125,5120,5832,6272,12500,

%T 21600,25600,30375,36000,46656,48600,77760,84375,114688,116640,121500,

%U 138240,169344,225000,247808,337500,384000,388800,395136,583200,600000,653184,691200,750141,802816,823543,857304,979776

%N Numbers k such that, in the prime factorization of k, the least common multiple of the exponents equals the least common multiple of the prime factors.

%C Numbers k such that A072411(k) = A007947(k). - _Michel Marcus_, Aug 29 2022

%C Terms p^p, p prime, form the subsequence A051674. - _Bernard Schott_, Sep 21 2022

%C Terms p^q * q^p with distinct primes p and q form the subsequence A082949. - _Bernard Schott_, Feb 01 2023

%e 576 = 2^6 * 3^2, lcm(2,3) = 6 = lcm(6,2), hence 576 is a term.

%t Select[Range[10^6], Equal @@ LCM @@ FactorInteger[#] &] (* _Amiram Eldar_, Aug 07 2022 *)

%o (PARI) isok(k) = my(f=factor(k)); lcm(f[,1]) == lcm(f[,2]); \\ _Michel Marcus_, Aug 07 2022

%o (Python)

%o from math import lcm

%o from sympy import factorint

%o def ok(n): f = factorint(n); return lcm(*f.keys()) == lcm(*f.values())

%o print([k for k in range(10**6) if ok(k)]) # _Michael S. Branicky_, Aug 07 2022

%Y Cf. A054411, A054412, A068935, A068936, A068937, A068938.

%Y Cf. A072411, A007947, A051674, A082949.

%K nonn

%O 1,2

%A _Jean-Marc Rebert_, Aug 07 2022