A375073 Numbers whose prime factorization exponents include at least one 2, at least one 3 and no other exponents.

72, 108, 200, 392, 500, 675, 968, 1125, 1323, 1352, 1372, 1800, 2312, 2700, 2888, 3087, 3267, 3528, 4232, 4500, 4563, 5292, 5324, 5400, 6125, 6728, 7688, 7803, 8575, 8712, 8788, 9000, 9747, 9800, 10584, 10952, 11979, 12168, 12348, 13068, 13448, 13500, 14283, 14792

Offset: 1

Author

Amiram Eldar, Jul 29 2024

Keywords

• nonn
• easy

Comments

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

Number k such that A051904(k) = 2 and A051903(k) = 3.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for sequences computed from exponents in factorization of n.

Crossrefs

Equals A338325 \ (A062503 UNION A062838).

Subsequence of A001694 and A046100.

A143610 is a subsequence.

Cf. A051903, A051904, A136568.

Cf. A082020, A157289, A330595.

Programs

Mathematica

Select[Range[15000], Union[FactorInteger[#][[;; , 2]]] == {2, 3} &]

PARI

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

Formula

Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + 1/p^2 + 1/p^3) - 15/Pi^2 - zeta(3)/zeta(6) + 1 = A330595 - A082020 - A157289 + 1 = 0.047550294197921818806... .