A375075 - OEIS

%I #6 Jul 30 2024 14:36:51

%S 360,504,540,600,756,792,936,1176,1188,1224,1350,1368,1400,1404,1500,

%T 1656,1836,1960,2052,2088,2200,2232,2250,2484,2520,2600,2646,2664,

%U 2904,2952,3096,3132,3348,3384,3400,3500,3780,3800,3816,3960,3996,4056,4116,4200,4248,4312,4392,4428

%N Numbers whose prime factorization exponents include at least one 1, at least one 2, at least one 3 and no other exponents.

%C First differs from its subsequence A163569 at n = 25: a(25) = 2520 = 2^3 * 3^2 * 5 * 7 is not a term of A163569.

%C Numbers k such that the set of distinct prime factorization exponents of k (row k of A136568) is {1, 2, 3}.

%C The asymptotic densities of this sequence and A375074 are equal (0.0156712..., see A375074 for a formula), since the terms in A375074 that are not in this sequence (A375073) have a density 0.

%H Amiram Eldar, <a href="/A375075/b375075.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>.

%t Select[Range[4500], Union[FactorInteger[#][[;; , 2]]] == {1, 2, 3} &]

%o (PARI) is(k) = Set(factor(k)[,2]) == [1, 2, 3];

%Y Intersection of A375072 and A317090.

%Y Equals A375074 \ A375073.

%Y Subsequence of A046100 and A176297.

%Y A163569 is a subsequence.

%Y Cf. A002117, A013661, A013662, A013664, A059956, A068468, A088453, A136568, A215267.

%K nonn,easy

%O 1,1

%A _Amiram Eldar_, Jul 29 2024