A356433 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.

1, 4, 27, 72, 108, 192, 576, 800, 1458, 1728, 2916, 3125, 5120, 5832, 6272, 12500, 21600, 25600, 30375, 36000, 46656, 48600, 77760, 84375, 114688, 116640, 121500, 138240, 169344, 225000, 247808, 337500, 384000, 388800, 395136, 583200, 600000, 653184, 691200, 750141, 802816, 823543, 857304, 979776

Offset: 1

Author

Jean-Marc Rebert, Aug 07 2022

Keywords

• nonn

Comments

Numbers k such that A072411(k) = A007947(k). - Michel Marcus, Aug 29 2022

Terms p^p, p prime, form the subsequence A051674. - Bernard Schott, Sep 21 2022

Terms p^q * q^p with distinct primes p and q form the subsequence A082949. - Bernard Schott, Feb 01 2023

Examples

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

Crossrefs

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

Cf. A072411, A007947, A051674, A082949.

Programs

Mathematica

Select[Range[10^6], Equal @@ LCM @@ FactorInteger[#] &] (* Amiram Eldar, Aug 07 2022 *)

PARI

isok(k) = my(f=factor(k)); lcm(f[,1]) == lcm(f[,2]); \\ Michel Marcus, Aug 07 2022

Python

from math import lcm
from sympy import factorint
def ok(n): f = factorint(n); return lcm(*f.keys()) == lcm(*f.values())
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Aug 07 2022