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%I #22 Sep 09 2022 04:20:03
%S 36,100,144,180,196,216,225,252,300,324,396,400,441,450,468,484,576,
%T 588,612,676,684,700,720,784,828,882,900,980,1000,1008,1044,1080,1089,
%U 1100,1116,1156,1200,1225,1260,1296,1300,1332,1444,1452,1476,1512,1521
%N Numbers k such that the LCM of exponents in the prime factorization of k does not equal the product of the exponents.
%C 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
%H Michael De Vlieger, <a href="/A072413/b072413.txt">Table of n, a(n) for n = 1..10000</a>
%F A005361(a(n)) != A072411(a(n)).
%e k = 36 = 2*2*3*3; exponent set = {2,2}; LCM = 2, product = 4.
%t Select[Range@ 1600, LCM @@ # != Times @@ # &@ Map[Last, FactorInteger@ #] &] (* _Michael De Vlieger_, May 15 2016 *)
%o (PARI) is(n)=my(f=factor(n)[,2]); n>9 && lcm(f)!=factorback(f) \\ _Charles R Greathouse IV_, Jan 14 2017
%Y Cf. A005361, A051903, A051904, A052409, A052486, A072411-A072414.
%K nonn
%O 1,1
%A _Labos Elemer_, Jun 17 2002
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