A092680 Numbers of the form 3*2^k with a single anti-divisor.

3, 6, 96, 393216

Offset: 1

Author

Lior Manor, Mar 03 2004

Keywords

• nonn
• hard
• more

Comments

See A066272 for definition of anti-divisor.

If it exists, a(5) > 3*2^(1000). See A092679. - J.W.L. (Jan) Eerland, Nov 13 2022

Crossrefs

Cf. A066272, A066466, A092679, A181490, A181491, A181492.

Programs

Python

from itertools import count, islice
from sympy.ntheory.factor_ import antidivisor_count
def A092680_gen(): return filter(lambda n: antidivisor_count(n)==1,(3*2**k for k in count(0)))
A092680_list = list(islice(A092680_gen(),4)) # Chai Wah Wu, Jan 04 2022

Formula

a(n) = 3*2^A092679(n).

a(n) = 3*2^(A181490(n)-1) = (A181491(n)+1)/2 = (A181492(n)-1)/2. - Max Alekseyev, Feb 14 2025