A375074 -id:A375074 - cp's OEIS frontend

A375075 Numbers whose prime factorization exponents include at least one 1, at least one 2, at least one 3 and no other exponents.

360, 504, 540, 600, 756, 792, 936, 1176, 1188, 1224, 1350, 1368, 1400, 1404, 1500, 1656, 1836, 1960, 2052, 2088, 2200, 2232, 2250, 2484, 2520, 2600, 2646, 2664, 2904, 2952, 3096, 3132, 3348, 3384, 3400, 3500, 3780, 3800, 3816, 3960, 3996, 4056, 4116, 4200, 4248, 4312, 4392, 4428

Offset: 1

Amiram Eldar, Jul 29 2024

First differs from its subsequence A163569 at n = 25: a(25) = 2520 = 2^3 * 3^2 * 5 * 7 is not a term of A163569.
Numbers k such that the set of distinct prime factorization exponents of k (row k of A136568) is {1, 2, 3}.
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.

Intersection of A375072 and A317090.
Equals A375074 \ A375073.
Subsequence of A046100 and A176297.
A163569 is a subsequence.
Cf. A002117, A013661, A013662, A013664, A059956, A068468, A088453, A136568, A215267.

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

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

cp's OEIS Frontend

A375075 Numbers whose prime factorization exponents include at least one 1, at least one 2, at least one 3 and no other exponents.

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