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

1,1

Links

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

Example

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

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 *)

Crossrefs

Cf. A167408 - Orderly Numbers

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

Cf. A167411 - Minimal K Values for the Orderly Numbers

Sequence in context: A365614 A074321 A253049 * A302340 A310003 A085378

Adjacent sequences: A167407 A167408 A167409 * A167411 A167412 A167413

Keyword

nonn

Author

Andrew Weimholt, Nov 03 2009

Status

approved