

A066467


Numbers having just two antidivisors.


1



5, 8, 9, 12, 16, 24, 36, 64, 576, 4096, 65536, 262144, 1073741824
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

See A066272 for definition of antidivisor.
a(14) > 5*10^11. 2^42*3^2, 2^62*3^2, 2^210*3^2, 2^60 and 2^126 are also terms. If 2*k1 and 2*k+1 are both prime and k has exactly three odd divisors, then k is a term. Also if 2^p1 is a Mersenne prime and 2^p+1 is the product of two distinct primes, then 2^(p1) is a term.  Donovan Johnson, Jan 21 2013


LINKS

Table of n, a(n) for n=1..13.
Jon Perry, The AntiDivisor
Jon Perry, The Antidivisor [Cached copy]
Jon Perry, The Antidivisor: Even More AntiDivisors [Cached copy]


MAPLE

A066467:= proc(q)
local k, n, t;
for n from 1 to q do
t:=0; for k from 2 to n1 do if abs((n mod k)k/2)<1 then t:=t+1; fi; od;
if t=2 then print(n); fi; od; end:
A066467 (10^10); # Paolo P. Lava, Feb 22 2013


MATHEMATICA

antid[n_] := Select[ Union[ Join[ Select[ Divisors[2n  1], OddQ[ # ] && # != 1 & ], Select[ Divisors[2n + 1], OddQ[ # ] && # != 1 & ], 2n/Select[ Divisors[ 2*n], OddQ[ # ] && # != 1 &]]] }, # < n & ]]; Select[ Range[10^5], Length[ antid[ # ]] == 2 & ]


PROG

(Python)
from sympy.ntheory.factor_ import antidivisor_count
A066467_list = [n for n in range(1, 10**5) if antidivisor_count(n) == 2]
# Chai Wah Wu, Jul 17 2015


CROSSREFS

Cf. A066272.
Sequence in context: A034812 A260256 A314573 * A180244 A072833 A229469
Adjacent sequences: A066464 A066465 A066466 * A066468 A066469 A066470


KEYWORD

nonn,more


AUTHOR

Robert G. Wilson v, Jan 02 2002


EXTENSIONS

a(12)a(13) from Donovan Johnson, Jun 19 2010


STATUS

approved



