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A072413
Numbers k such that the LCM of exponents in the prime factorization of k does not equal the product of the exponents.
3
36, 100, 144, 180, 196, 216, 225, 252, 300, 324, 396, 400, 441, 450, 468, 484, 576, 588, 612, 676, 684, 700, 720, 784, 828, 882, 900, 980, 1000, 1008, 1044, 1080, 1089, 1100, 1116, 1156, 1200, 1225, 1260, 1296, 1300, 1332, 1444, 1452, 1476, 1512, 1521
OFFSET
1,1
COMMENTS
The numbers of terms not exceeding 10^k, for k = 2, 3, ..., are 2, 29, 348, 3548, 35761, 358258, 3583892, 35843109, 358440763, ... . Apparently, the asymptotic density of this sequence exists and equals 0.03584... . - Amiram Eldar, Sep 09 2022
LINKS
FORMULA
A005361(a(n)) != A072411(a(n)).
EXAMPLE
k = 36 = 2*2*3*3; exponent set = {2,2}; LCM = 2, product = 4.
MATHEMATICA
Select[Range@ 1600, LCM @@ # != Times @@ # &@ Map[Last, FactorInteger@ #] &] (* Michael De Vlieger, May 15 2016 *)
PROG
(PARI) is(n)=my(f=factor(n)[, 2]); n>9 && lcm(f)!=factorback(f) \\ Charles R Greathouse IV, Jan 14 2017
KEYWORD
nonn
AUTHOR
Labos Elemer, Jun 17 2002
STATUS
approved