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A066467 Numbers having just two anti-divisors. 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 anti-divisor.

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*k-1 and 2*k+1 are both prime and k has exactly three odd divisors, then k is a term. Also if 2^p-1 is a Mersenne prime and 2^p+1 is the product of two distinct primes, then 2^(p-1) is a term. - Donovan Johnson, Jan 21 2013

LINKS

Table of n, a(n) for n=1..13.

Jon Perry, The Anti-Divisor

Jon Perry, The Anti-divisor [Cached copy]

Jon Perry, The Anti-divisor: Even More Anti-Divisors [Cached copy]

MAPLE

A066467:= proc(q)

local k, n, t;

for n from 1 to q do

t:=0; for k from 2 to n-1 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: A100832 A034812 A260256 * 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

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Last modified February 24 12:46 EST 2018. Contains 299623 sequences. (Running on oeis4.)