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Least number k such that k has n anti-divisors.
2

%I #7 Mar 30 2012 17:30:38

%S 1,3,5,7,13,17,32,38,85,67,162,137,338,203,760,247,1225,472,578,682,

%T 1012,787,9112,1463,2048,2047,2888,2363,5513,3465,5512,6682,8978,5197,

%U 17672,5198,71442,9653,29768,8662,40898,13513,81608,15593,131072,35437

%N Least number k such that k has n anti-divisors.

%C See A066272 for definition of anti-divisor.

%H Donovan Johnson, <a href="/A066464/b066464.txt">Table of n, a(n) for n = 0..400</a>

%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 & ]]; a = Table[0, {50} ]; Do[ b = Length[ antid[n]]; If[ a[[b + 1]] == 0 && b < 50, a[[b + 1]] = n], {n, 1, 2^17} ]; a

%Y Cf. A066272.

%K nonn

%O 0,2

%A _Robert G. Wilson v_, Jan 02 2002