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

1,1

Comments

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.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from exponents in factorization of n.

Mathematica

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

Prog

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

Crossrefs

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.

Sequence in context: A060665 A323024 A072414 * A163569 A063067 A076205

Adjacent sequences: A375072 A375073 A375074 * A375076 A375077 A375078

Keyword

nonn,easy,new

Author

Amiram Eldar, Jul 29 2024

Status

approved