|
%I #8 Jul 30 2024 14:36:33
%S 72,108,200,360,392,500,504,540,600,675,756,792,936,968,1125,1176,
%T 1188,1224,1323,1350,1352,1368,1372,1400,1404,1500,1656,1800,1836,
%U 1960,2052,2088,2200,2232,2250,2312,2484,2520,2600,2646,2664,2700,2888,2904,2952,3087
%N Numbers whose prime factorization exponents include at least one 2, at least one 3 and no higher exponents.
%C Numbers whose powerful part (A057521) is a term of A375073.
%C The asymptotic density of this sequence is 1/zeta(4) - 1/zeta(3) + 1/zeta(2) - zeta(6)/(zeta(2) * zeta(3)) * c = A215267 - A088453 + A059956 - A068468 * c = 0.0156712080080470088619..., where c = Product_{p prime} (1 + 2/p^3 - 1/p^4 + 1/p^5).
%H Amiram Eldar, <a href="/A375074/b375074.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%F A051903(a(n)) = 3.
%t Select[Range[3000], Union[Select[FactorInteger[#][[;; , 2]], # > 1 &]] == {2, 3} &]
%o (PARI) is(k) = Set(select(x -> x > 1, factor(k)[,2])) == [2, 3];
%Y Equals A046100 \ (A004709 UNION A336591).
%Y Disjoint union of A375073 and A375075.
%Y Cf. A051903, A057521.
%Y Cf. A002117, A013661, A013662, A013664, A059956, A068468, A088453, A215267.
%K nonn,easy,new
%O 1,1
%A _Amiram Eldar_, Jul 29 2024
|
