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A336066 Numbers k such that the exponent of the highest power of 2 dividing k (A007814) is a divisor of k.

%I A336066 #15 Jul 10 2022 13:24:02
%S A336066 2,4,6,10,12,14,16,18,20,22,24,26,28,30,34,36,38,42,44,46,48,50,52,54,
%T A336066 58,60,62,66,68,70,72,74,76,78,80,82,84,86,90,92,94,98,100,102,106,
%U A336066 108,110,112,114,116,118,120,122,124,126,130,132,134,138,140,142,144
%N A336066 Numbers k such that the exponent of the highest power of 2 dividing k (A007814) is a divisor of k.
%C A336066 All the terms are even by definition.
%C A336066 If m is a term then m*(2*k+1) is a term for all k>=1.
%C A336066 Šalát (1994) proved that the asymptotic density of this sequence is 0.435611... (A336067).
%H A336066 Amiram Eldar, <a href="/A336066/b336066.txt">Table of n, a(n) for n = 1..10000</a>
%H A336066 Tibor Šalát, <a href="https://dml.cz/handle/10338.dmlcz/129777">On the function a_p, p^a_p(n) || n (n > 1)</a>, Mathematica Slovaca, Vol. 44, No. 2 (1994), pp. 143-151.
%e A336066 2 is a term since A007814(2) = 1 is a divisor of 2.
%t A336066 Select[Range[2, 150, 2], Divisible[#, IntegerExponent[#, 2]] &]
%o A336066 (PARI) isok(m) = if (!(m%2), (m % valuation(m,2)) == 0); \\ _Michel Marcus_, Jul 08 2020
%o A336066 (Python)
%o A336066 from itertools import count, islice
%o A336066 def A336066_gen(startvalue=2): # generator of terms >= startvalue
%o A336066     return filter(lambda n:n%(~n&n-1).bit_length()==0,count(max(startvalue+startvalue&1,2),2))
%o A336066 A336066_list = list(islice(A336066_gen(startvalue=3),30)) # _Chai Wah Wu_, Jul 10 2022
%Y A336066 A001146 and A039956 are subsequences.
%Y A336066 Cf. A007814, A336067.
%Y A336066 Similar sequences: A033950, A005349, A006446, A074946, A075592, A007694, A112249, A336068.
%K A336066 nonn
%O A336066 1,1
%A A336066 _Amiram Eldar_, Jul 07 2020