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

%I #29 Feb 14 2025 08:26:15

%S 3,6,96,393216

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

%C See A066272 for definition of anti-divisor.

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

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

%F a(n) = 3*2^(A181490(n)-1) = (A181491(n)+1)/2 = (A181492(n)-1)/2. - _Max Alekseyev_, Feb 14 2025

%o (Python)

%o from itertools import count, islice

%o from sympy.ntheory.factor_ import antidivisor_count

%o def A092680_gen(): return filter(lambda n: antidivisor_count(n)==1,(3*2**k for k in count(0)))

%o A092680_list = list(islice(A092680_gen(),4)) # _Chai Wah Wu_, Jan 04 2022

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

%K nonn,hard,more,changed

%O 1,1

%A _Lior Manor_, Mar 03 2004