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A375073
Numbers whose prime factorization exponents include at least one 2, at least one 3 and no other exponents.
4
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.
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.
Sequence in context: A114128 A375074 A375143 * A143610 A166987 A339940
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Jul 29 2024
STATUS
approved