login
A162643
Numbers whose number of divisors is not a power of 2.
18
4, 9, 12, 16, 18, 20, 25, 28, 32, 36, 44, 45, 48, 49, 50, 52, 60, 63, 64, 68, 72, 75, 76, 80, 81, 84, 90, 92, 96, 98, 99, 100, 108, 112, 116, 117, 121, 124, 126, 132, 140, 144, 147, 148, 150, 153, 156, 160, 162, 164, 169, 171, 172, 175, 176, 180, 188, 192, 196, 198
OFFSET
1,1
COMMENTS
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
The asymptotic density of this sequence is 1 - A327839 = 0.3121728605... - Amiram Eldar, Jul 28 2020
LINKS
FORMULA
A209229(A000005(a(n))) = 0. - Reinhard Zumkeller, Nov 15 2012
MATHEMATICA
Select[Range@ 192, ! IntegerQ@ Log2@ DivisorSigma[0, #] &] (* Michael De Vlieger, Feb 24 2017 *)
PROG
(Haskell)
a162643 n = a162643_list !! (n-1)
a162643_list = filter ((== 0) . a209229 . a000005) [1..]
-- Reinhard Zumkeller, Nov 15 2012
(Python)
from itertools import count, islice
from sympy import factorint
def A162643_gen(startvalue=1): # generator of terms >= startvalue
return filter(lambda n:any(map(lambda m:((k:=m+1)&-k)^k, factorint(n).values())), count(max(startvalue, 1)))
A162643_list = list(islice(A162643_gen(), 30)) # Chai Wah Wu, Jan 04 2023
CROSSREFS
Complement of A036537.
A072587 is a subsequence.
Sequence in context: A355571 A376164 A072498 * A072587 A240112 A368714
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jul 08 2009
STATUS
approved