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

1,2

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

Links

Table of n, a(n) for n=1..44.

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

Cf. A072411, A007947, A051674, A082949.

Sequence in context: A158186 A272858 A272818 * A272859 A054412 A122405

Adjacent sequences: A356430 A356431 A356432 * A356434 A356435 A356436

Keyword

nonn

Author

Jean-Marc Rebert, Aug 07 2022

Status

approved