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%I #19 Feb 23 2024 01:09:58
%S 32,49,50,60,72,81,121,128,145,180,181,196,264,288,324,361,480,529,
%T 684,685,961,1156,1405,2304,2401,2500,2521,2704,2809,4624,4705,5041,
%U 5184,7396,8064,8581,9385,10816,11881,13456,14281,25600,26569,27556,34585
%N Numbers having exactly six anti-divisors.
%C See A066272 for definition of anti-divisor.
%H Chai Wah Wu, <a href="/A066472/b066472.txt">Table of n, a(n) for n = 1..1000</a>
%H Jon Perry, <a href="http://www.users.globalnet.co.uk/~perry/maths/antidivisor.htm">The Anti-Divisor</a> [broken link; see below]
%H Jon Perry, <a href="/A066272/a066272a.html">The Anti-divisor</a> [Cached copy]
%H Jon Perry, <a href="/A066272/a066272.html">The Anti-divisor: Even More Anti-Divisors</a> [Cached copy]
%t 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[10^4], Length[ antid[ # ]] == 6 & ]
%o (Python)
%o from sympy.ntheory.factor_ import antidivisor_count
%o A066472_list = [n for n in range(1,10**5) if antidivisor_count(n) == 6] # _Chai Wah Wu_, Jul 25 2015
%Y Cf. A066272.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Jan 02 2002
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