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

1,1

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.

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... .

Mathematica

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

Prog

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

Crossrefs

Equals A338325 \ (A062503 UNION A062838).

Subsequence of A001694 and A046100.

A143610 is a subsequence.

Cf. A051903, A051904, A136568.

Cf. A082020, A157289, A330595.

Sequence in context: A114128 A375074 A375143 * A143610 A166987 A339940

Adjacent sequences: A375070 A375071 A375072 * A375074 A375075 A375076

Keyword

nonn,easy,new

Author

Amiram Eldar, Jul 29 2024

Status

approved