A365408 - OEIS

%I #21 Oct 19 2023 19:53:39

%S 9,12,15,18,21,25,27,30,33,35,36,39,40,42,45,48,49,50,51,54,55,56,57,

%T 60,63,65,66,69,70,75,77,78,81,84,85,87,90,91,93,95,98,99,100,102,105,

%U 108,110,111,114,115,117,119,120,121,123,125,126,129,130,132,133,135,138,140,141,143,144,145,147,150,153

%N Numbers j whose largest divisor <= sqrt(j) is not a power of 2.

%C Also indices of terms in A033676 that are not a power of 2.

%C Differs from A342082 in not having {24, 72, 80, 96, 112, ...}. - _Hugo Pfoertner_, Oct 15 2023

%H Paolo Xausa, <a href="/A365408/b365408.txt">Table of n, a(n) for n = 1..10000</a>

%t A365408Q[n_]:=With[{d=Divisors[n]},!IntegerQ[Log2[d[[Ceiling[Length[d]/2]]]]]];

%t Select[Range[200],A365408Q] (* _Paolo Xausa_, Oct 19 2023 *)

%o (Python)

%o from itertools import count, islice

%o from sympy import divisors

%o def A365408_gen(startvalue=1): # generator of terms >= startvalue

%o     return filter(lambda i:(a:=(d:=divisors(i))[len(d)-1>>1])!=1<<a.bit_length()-1,count(max(startvalue,1)))

%o A365408_list = list(islice(A365408_gen(),30)) # _Chai Wah Wu_, Oct 18 2023

%Y Complement of A365406.

%Y Cf. A033676, A057716, A342082.

%K nonn

%O 1,1

%A _Omar E. Pol_, Oct 14 2023