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Numbers having just three anti-divisors.
0

%I #10 Feb 25 2024 05:58:16

%S 7,10,11,14,15,19,20,21,26,29,30,34,44,48,51,54,56,69,79,89,106,114,

%T 120,134,141,146,156,174,191,216,224,244,251,271,296,309,316,321,359,

%U 376,384,386,394,404,411,439,496,516,524,596,601,614,659,664,691,719

%N Numbers having just three anti-divisors.

%C See A066272 for definition of anti-divisor.

%H Jon Perry, <a href="http://www.users.globalnet.co.uk/~perry/maths/antidivisor.htm">The Anti-Divisor</a>

%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[ # ]] == 3 & ]

%Y Cf. A066272.

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Jan 02 2002