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

1,1

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).

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.

Example

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

Mathematica

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

Prog

(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

Crossrefs

A001146 and A039956 are subsequences.

Cf. A007814, A336067.

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

Sequence in context: A226295 A090127 A057910 * A120351 A022305 A103799

Adjacent sequences: A336063 A336064 A336065 * A336067 A336068 A336069

Keyword

nonn

Author

Amiram Eldar, Jul 07 2020

Status

approved