
COMMENTS

See A167408 for the definition of Orderly.
All doubly orderly numbers are orderly modulo k=tau(n)+1 and k=tau(n)+3, and are also "very orderly" (Cf. A167409).
Composite numbers appearing in both A167409 and A168003.
No composite number is orderly for more than two values of k, and 11 is the only prime which is orderly for exactly two values of k. 11 does not appear in this sequence as the definition of "doubly orderly" applies only to composite numbers.


EXAMPLE

393625 is in the list because it is orderly modulo 17 and 19
.{1,1175,15745,3149,5,125,393625,25,1675,5875,8375,335,47,235,78725,67} == {1,2,3,...,16} mod 17
.{1,393625,1675,5875,5,25,235,78725,47,67,125,335,15745,3149,8375,1175} == {1,2,3,...,16} mod 19
