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A162643 Numbers whose number of divisors is not a power of 2.

%I A162643 #29 Jan 04 2023 15:04:59
%S A162643 4,9,12,16,18,20,25,28,32,36,44,45,48,49,50,52,60,63,64,68,72,75,76,
%T A162643 80,81,84,90,92,96,98,99,100,108,112,116,117,121,124,126,132,140,144,
%U A162643 147,148,150,153,156,160,162,164,169,171,172,175,176,180,188,192,196,198
%N A162643 Numbers whose number of divisors is not a power of 2.
%C A162643 A number m is a term if and only if it has at least one non-infinitary divisor, or A000005(m) > A037445(m). - _Vladimir Shevelev_, Feb 23 2017
%C A162643 The asymptotic density of this sequence is 1 - A327839 = 0.3121728605... - _Amiram Eldar_, Jul 28 2020
%H A162643 Reinhard Zumkeller, <a href="/A162643/b162643.txt">Table of n, a(n) for n = 1..10000</a>
%F A162643 A209229(A000005(a(n))) = 0. - _Reinhard Zumkeller_, Nov 15 2012
%t A162643 Select[Range@ 192, ! IntegerQ@ Log2@ DivisorSigma[0, #] &] (* _Michael De Vlieger_, Feb 24 2017 *)
%o A162643 (Haskell)
%o A162643 a162643 n = a162643_list !! (n-1)
%o A162643 a162643_list = filter ((== 0) . a209229 . a000005) [1..]
%o A162643 -- _Reinhard Zumkeller_, Nov 15 2012
%o A162643 (Python)
%o A162643 from itertools import count, islice
%o A162643 from sympy import factorint
%o A162643 def A162643_gen(startvalue=1): # generator of terms >= startvalue
%o A162643     return filter(lambda n:any(map(lambda m:((k:=m+1)&-k)^k,factorint(n).values())),count(max(startvalue,1)))
%o A162643 A162643_list = list(islice(A162643_gen(),30)) # _Chai Wah Wu_, Jan 04 2023
%Y A162643 Complement of A036537.
%Y A162643 A072587 is a subsequence.
%Y A162643 Cf. A000005, A037445, A209229, A327839
%K A162643 nonn
%O A162643 1,1
%A A162643 _Reinhard Zumkeller_, Jul 08 2009