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

2, 4, 6, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 34, 36, 38, 42, 44, 46, 48, 50, 52, 54, 58, 60, 62, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 90, 92, 94, 98, 100, 102, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 130, 132, 134, 138, 140, 142, 144

Offset: 1

Author

Amiram Eldar, Jul 07 2020

Keywords

• nonn

Comments

All the terms are even by definition.

If m is a term then m*(2*k+1) is a term for all k>=1.

Šalát (1994) proved that the asymptotic density of this sequence is 0.435611... (A336067).

Examples

			2 is a term since A007814(2) = 1 is a divisor of 2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Tibor Šalát, On the function a_p, p^a_p(n) || n (n > 1), Mathematica Slovaca, Vol. 44, No. 2 (1994), pp. 143-151.

Crossrefs

A001146 and A039956 are subsequences.

Cf. A007814, A336067.

Similar sequences: A033950, A005349, A006446, A074946, A075592, A007694, A112249, A336068.

Programs

Mathematica

Select[Range[2, 150, 2], Divisible[#, IntegerExponent[#, 2]] &]

PARI

isok(m) = if (!(m%2), (m % valuation(m,2)) == 0); \\ Michel Marcus, Jul 08 2020

Python

from itertools import count, islice
def A336066_gen(startvalue=2): # generator of terms >= startvalue
    return filter(lambda n:n%(~n&n-1).bit_length()==0,count(max(startvalue+startvalue&1,2),2))
A336066_list = list(islice(A336066_gen(startvalue=3),30)) # Chai Wah Wu, Jul 10 2022