OFFSET
1,2
COMMENTS
The very orderly numbers are orderly numbers (cf. A167408) with K = tau(N) + 1.
Equivalently, all divisors must be pairwise distinct and distinct from 0, modulo tau(N) = number of divisors of N. - M. F. Hasler, Mar 21 2023
LINKS
Andrew Weimholt, Table of n, a(n) for n = 1..10000
EXAMPLE
12 is in the sequence as it has the 6 divisors {1, 2, 3, 4, 12, 6} which when reduced mod (6+1) give {1, 2, 3, 4, 5, 6} = {1, 2, ..., tau(12)}. - David A. Corneth, Mar 21 2023
MATHEMATICA
veryOrderlyQ[n_] := (If[tau = DivisorSigma[0, n]; Union[Mod[Divisors[n], tau + 1]] == Range[tau], Return[True]]; False); Select[ Range[260], veryOrderlyQ] (* Jean-François Alcover, Aug 19 2013 *)
PROG
(PARI) select( {vo(n)=#(n=divisors(n))==#(n=Set(n%(1+#n))) && n[1]}, [1..999]) \\ M. F. Hasler; updated for current PARI syntax Mar 21 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Weimholt, Nov 03 2009
STATUS
approved