A375074 Numbers whose prime factorization exponents include at least one 2, at least one 3 and no higher exponents.

72, 108, 200, 360, 392, 500, 504, 540, 600, 675, 756, 792, 936, 968, 1125, 1176, 1188, 1224, 1323, 1350, 1352, 1368, 1372, 1400, 1404, 1500, 1656, 1800, 1836, 1960, 2052, 2088, 2200, 2232, 2250, 2312, 2484, 2520, 2600, 2646, 2664, 2700, 2888, 2904, 2952, 3087

Offset

1,1

Comments

Numbers whose powerful part (A057521) is a term of A375073.

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).

Links

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

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

Formula

A051903(a(n)) = 3.

Mathematica

Select[Range[3000], Union[Select[FactorInteger[#][[;; , 2]], # > 1 &]] == {2, 3} &]

Prog

(PARI) is(k) = Set(select(x -> x > 1, factor(k)[, 2])) == [2, 3];

Crossrefs

Equals A046100 \ (A004709 UNION A336591).

Disjoint union of A375073 and A375075.

Cf. A051903, A057521.

Cf. A002117, A013661, A013662, A013664, A059956, A068468, A088453, A215267.

Sequence in context: A052486 A378859 A114128 * A375143 A375073 A143610

Adjacent sequences: A375071 A375072 A375073 * A375075 A375076 A375077

Keyword

nonn,easy

Author

Amiram Eldar, Jul 29 2024

Status

approved