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Numbers whose prime factorization exponents include at least one 2, at least one 3 and no other exponents.
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%I #8 Jul 30 2024 14:36:22

%S 72,108,200,392,500,675,968,1125,1323,1352,1372,1800,2312,2700,2888,

%T 3087,3267,3528,4232,4500,4563,5292,5324,5400,6125,6728,7688,7803,

%U 8575,8712,8788,9000,9747,9800,10584,10952,11979,12168,12348,13068,13448,13500,14283,14792

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

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

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

%H Amiram Eldar, <a href="/A375073/b375073.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.

%F 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... .

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

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

%Y Equals A338325 \ (A062503 UNION A062838).

%Y Subsequence of A001694 and A046100.

%Y A143610 is a subsequence.

%Y Cf. A051903, A051904, A136568.

%Y Cf. A082020, A157289, A330595.

%K nonn,easy

%O 1,1

%A _Amiram Eldar_, Jul 29 2024