A167411 a(n) = the minimal K value for the orderly number A167408(n).

2, 3, 3, 5, 5, 7, 3, 7, 11, 3, 17, 7, 3, 5, 3, 29, 5, 5, 3, 41, 3, 7, 3, 5, 5, 3, 59, 5, 7, 3, 13, 71, 7, 7, 3, 5, 3, 5, 3, 101, 3, 107, 3, 7, 5, 7, 5, 3, 5, 3, 137, 3, 149, 5, 5, 11, 7, 7, 3, 3, 5, 5, 3, 179, 7, 3, 191, 3, 197, 5, 11, 5, 13, 3, 227, 3, 7, 5, 3, 239, 7, 7, 5, 3, 11, 3, 3, 5, 3

Offset: 1

Author

Andrew Weimholt, Nov 03 2009

Keywords

• nonn

Examples

			a(6) = 7, because A167408(6) = 9, and divisors of 9 = {1,9,3} == {1,2,3} mod 7.
		

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. A167410 - Disorderly Numbers - numbers not in A167408.

Programs

Mathematica

orderlyQkValue[n_] := (For[dd = Divisors[n]; tau = Length[dd]; k = 2, k <= Max[tau + 4, Last[dd] - 2], k++, If[Union[Mod[dd, k]] == Range[tau], Return[{True, k}]]]; {False, 0}); A167411List = Select[{#, orderlyQkValue[#]}& /@ Range[400] , #[[2, 1]]&][[All, 2, 2]] (* Jean-François Alcover, Nov 03 2016 *)