A375076 - OEIS

%I #10 Jul 30 2024 14:37:02

%S 24,40,54,56,88,104,120,135,136,152,168,184,189,232,248,250,264,270,

%T 280,296,297,312,328,344,351,375,376,378,408,424,440,456,459,472,488,

%U 513,520,536,552,568,584,594,616,621,632,664,680,686,696,702,712,728,744,750

%N Numbers whose prime factorization exponents include at least one 1, at least one 3 and no other exponents.

%C First differs from its subsequence A360793 at n = 79: a(79) = 1080 = 2^3 * 3^3 * 5 is not a term of A360793.

%C Numbers k such that the set of distinct prime factorization exponents of k (row k of A136568) is {1, 3}.

%C The asymptotic density of this sequence is ((zeta(6)/zeta(3)) * Product_{p prime} (1 + 2/p^3 - 1/p^4 + 1/p^5) - 1)/zeta(2) = 0.076359822332835689478... .

%H Amiram Eldar, <a href="/A375076/b375076.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>.

%t Select[Range[750], Union[FactorInteger[#][[;; , 2]]] == {1, 3} &]

%o (PARI) is(k) = Set(factor(k)[,2]) == [1, 3];

%Y Equals A336591 \ (A005117 UNION A062838).

%Y Subsequences: A065036, A360793.

%Y Cf. A002117, A013661, A013664, A136568.

%K nonn,easy

%O 1,1

%A _Amiram Eldar_, Jul 29 2024