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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.
0
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
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
KEYWORD
nonn
AUTHOR
Jean-Marc Rebert, Aug 07 2022
STATUS
approved