A375075 -id:A375075 - cp's OEIS frontend

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

Amiram Eldar, Jul 29 2024

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).

Equals A046100 \ (A004709 UNION A336591).
Disjoint union of A375073 and A375075.
Cf. A051903, A057521.
Cf. A002117, A013661, A013662, A013664, A059956, A068468, A088453, A215267.

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

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

A051903(a(n)) = 3.

cp's OEIS Frontend

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

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