A167410 Disorderly Numbers: numbers not in A167408 (orderly numbers).

3, 4, 6, 10, 14, 15, 16, 18, 21, 22, 24, 25, 26, 28, 30, 32, 33, 34, 35, 36, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 54, 55, 56, 60, 62, 63, 64, 65, 66, 69, 70, 74, 75, 77, 78, 80, 81, 82, 84, 85, 86, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 102, 104, 105, 106, 108

Offset: 1

Author

Andrew Weimholt, Nov 03 2009

Keywords

• nonn

Examples

			3 is disorderly because there exists no K > 2=tau(3), such that {1,3} == {1,2} mod K.
		

Links

• A. Weimholt, Table of n, a(n) for n=1,...,10000

Crossrefs

Cf. A167408 - Orderly Numbers

Cf. A167409 - Very Orderly Numbers ( K = tau(N)+1 )

Cf. A167411 - Minimal K Values for the Orderly Numbers

Programs

Mathematica

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 *)