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A322448 Numbers whose prime factorization contains at least one composite exponent.

%I A322448 #14 Dec 02 2020 03:19:27
%S A322448 16,48,64,80,81,112,144,162,176,192,208,240,256,272,304,320,324,336,
%T A322448 368,400,405,432,448,464,496,512,528,560,567,576,592,624,625,648,656,
%U A322448 688,704,720,729,752,768,784,810,816,832,848,880,891,912,944,960,976,1008
%N A322448 Numbers whose prime factorization contains at least one composite exponent.
%C A322448 The asymptotic density of this sequence is Product_{p prime} (1 - 1/p^4 + Sum_{q prime >= 5} 1/p^q - 1/p^(q-1)) = 0.05328066264472198953... (using the method of Shevelev, 2016). - _Amiram Eldar_, Nov 08 2020
%H A322448 Alois P. Heinz, <a href="/A322448/b322448.txt">Table of n, a(n) for n = 1..10000</a>
%H A322448 Vladimir Shevelev, <a href="https://arxiv.org/abs/1602.04244">A fast computation of density of exponentially S-numbers</a>, arXiv:1602.04244 [math.NT], 2016.
%e A322448 16 = 2^4 is a term because 4 is a composite exponent here.
%p A322448 a:= proc(n) option remember; local k; for k from 1+
%p A322448       `if`(n=1, 0, a(n-1)) while andmap(i-> i[2]=1 or
%p A322448        isprime(i[2]), ifactors(k)[2]) do od; k
%p A322448     end:
%p A322448 seq(a(n), n=1..70);
%t A322448 Select[Range[1000], AnyTrue[FactorInteger[#][[;; , 2]], CompositeQ] &] (* _Amiram Eldar_, Nov 08 2020 *)
%o A322448 (PARI) isok(m) = #select(x->((x>1) && !isprime(x)), factor(m)[,2]) > 0; \\ _Michel Marcus_, Dec 02 2020
%Y A322448 Cf. A002808, A322449.
%K A322448 nonn
%O A322448 1,1
%A A322448 _Alois P. Heinz_, Dec 08 2018