A317616 - OEIS

%I #12 Sep 25 2024 10:28:03

%S 12,18,20,24,28,40,44,45,48,50,52,54,56,60,63,68,75,76,80,84,88,90,92,

%T 96,98,99,104,112,116,117,120,124,126,132,135,136,140,144,147,148,150,

%U 152,153,156,160,162,164,168,171,172,175,176,180,184,188,189,192

%N Numbers whose prime multiplicities are not pairwise indivisible.

%C The numbers of terms that do not exceed 10^k, for k = 2, 3, ..., are 26, 344, 3762, 38711, 390527, 3915874, 39192197, 392025578, 3920580540, ... . Apparently, the asymptotic density of this sequence exists and equals 0.392... .  - _Amiram Eldar_, Sep 25 2024

%H Amiram Eldar, <a href="/A317616/b317616.txt">Table of n, a(n) for n = 1..10000</a>

%e 72 = 2^3 * 3^2 is not in the sequence because 3 and 2 are pairwise indivisible.

%t Select[Range[100],!Select[Tuples[Last/@FactorInteger[#],2],And[UnsameQ@@#,Divisible@@#]&]=={}&]

%o (PARI) is(k) = if(k == 1, 0, my(e = Set(factor(k)[,2])); if(vecmax(e) == 1, 0, for(i = 1, #e, for(j = 1, i-1, if(!(e[i] % e[j]), return(1)))); 0)); \\ _Amiram Eldar_, Sep 25 2024

%Y Cf. A118914, A124010, A285572, A285573, A303362, A304713, A316475, A317101, A317102.

%K nonn

%O 1,1

%A _Gus Wiseman_, Aug 01 2018