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%I #6 Nov 03 2016 04:38:10
%S 3,4,6,10,14,15,16,18,21,22,24,25,26,28,30,32,33,34,35,36,39,40,42,44,
%T 45,46,48,49,50,51,54,55,56,60,62,63,64,65,66,69,70,74,75,77,78,80,81,
%U 82,84,85,86,88,90,91,92,93,94,95,96,98,99,100,102,104,105,106,108
%N Disorderly Numbers: numbers not in A167408 (orderly numbers).
%H A. Weimholt, <a href="/A167410/b167410.txt">Table of n, a(n) for n=1,...,10000</a>
%e 3 is disorderly because there exists no K > 2=tau(3), such that {1,3} == {1,2} mod K.
%t orderlyQ[n_] := (For[dd = Divisors[n]; tau = Length[dd]; k = 3, k <= Max[tau + 4, Last[dd] - 2], k++, If[Union[Mod[dd, k]] == Range[tau], Return[True]]]; False); Select[Range[120], !orderlyQ[#]&] (* _Jean-François Alcover_, Nov 03 2016 *)
%Y Cf. A167408 - Orderly Numbers
%Y Cf. A167409 - Very Orderly Numbers ( K = tau(N)+1 )
%Y Cf. A167411 - Minimal K Values for the Orderly Numbers
%K nonn
%O 1,1
%A _Andrew Weimholt_, Nov 03 2009
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