A023534 Numbers k such that the largest power of 2 dividing k equals 2^omega(k).

1, 2, 12, 20, 28, 36, 44, 52, 68, 76, 92, 100, 108, 116, 120, 124, 148, 164, 168, 172, 188, 196, 212, 236, 244, 264, 268, 280, 284, 292, 312, 316, 324, 332, 356, 360, 388, 404, 408, 412, 428, 436, 440, 452, 456, 484, 500, 504, 508, 520, 524, 548, 552, 556

Offset

1,2

Comments

That is, numbers k such that A001221(k) is equal to A007814(k), where A001221(k) = omega(k) is the number of distinct primes dividing k, and A007814(k) is the exponent of the highest power of 2 dividing k.

Numbers k that are unitarily divisible by the number of unitary divisors of k (A034444), i.e., numbers k such that A034444(k) is a unitary divisor of k. Subsequence of A048166. - Amiram Eldar, Aug 15 2025

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from G. C. Greubel)

Example

omega(12) = 2 and 4 = 2^2 is the largest power of 2 dividing 12, hence 12 is in the sequence.

Mathematica

Select[Range[600], IntegerExponent[#, 2]==PrimeNu[#]&] (* Harvey P. Dale, Jun 26 2011 *)

Prog

(PARI) isok(n) = omega(n) == valuation(n, 2); \\ Michel Marcus, Apr 16 2015
(Python)
from itertools import count, islice
from sympy.ntheory.factor_ import primenu
def A023534_gen(startvalue=1): # generator of terms
    return filter(lambda n:(~n & n-1).bit_length() == primenu(n), count(max(startvalue, 1)))
A023534_list = list(islice(A023534_gen(), 30)) # Chai Wah Wu, Jul 05 2022

Crossrefs

Cf. A039700, A001221 (omega), A007814 (2-adic valuation), A034444, A048166.

Sequence in context: A137311 A032407 A136725 * A286683 A326238 A226399

Adjacent sequences: A023531 A023532 A023533 * A023535 A023536 A023537

Keyword

nonn

Author

Benoit Cloitre, Sep 04 2002

Status

approved