%I #11 Aug 02 2024 03:01:28

%S 8,16,24,27,32,40,48,54,56,64,72,80,81,88,96,104,108,112,120,125,128,

%T 135,136,144,152,160,162,168,176,184,189,192,200,208,224,232,240,243,

%U 248,250,256,264,270,272,280,288,296,297,304,312,320,324,328,336,343,344

%N Numbers whose prime factorization has exactly one exponent that is larger than 2.

%C Subsequence of A046099 and first differs from it at n = 35: A046099(35) = 216 = 2^3 * 3^3 is not a term of this sequence.

%C Numbers k such that the powerful part of k, A057521(k), is a prime power whose exponent is larger than 2 (A246549).

%C The asymptotic density of this sequence is (1/zeta(3)) * Sum_{p prime} 1/(p^3-1) = A286229 / A002117 = 0.16148833663564192901... .

%H Amiram Eldar, <a href="/A375145/b375145.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>.

%e 8 = 2^3 is a term since its prime factorization has exactly one exponent, 3, that is larger than 2.

%t q[n_] := Count[FactorInteger[n][[;; , 2]], _?(# > 2 &)] == 1; Select[Range[350], q]

%o (PARI) is(k) = #select(x -> x > 2, factor(k)[, 2]) == 1;

%Y Subsequence of A046099.

%Y Cf. A002117, A057521, A190641, A246549, A286229, A375146.

%K nonn,easy

%O 1,1

%A _Amiram Eldar_, Aug 01 2024