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A167409
Very orderly numbers: a number N is "very orderly" if the set of the divisors of N is congruent to the set {1,2,...,tau(N)} mod (tau(N) + 1).
6
1, 2, 5, 8, 11, 12, 17, 20, 23, 27, 29, 38, 41, 47, 52, 53, 57, 58, 59, 68, 71, 72, 76, 83, 87, 89, 101, 107, 113, 117, 118, 124, 131, 133, 137, 149, 158, 162, 164, 167, 173, 177, 178, 179, 188, 191, 197, 203, 218, 227, 233, 236, 237, 239, 243, 244, 247, 251, 257
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
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
Cf. A167408 (orderly numbers), A167410 (disorderly numbers).
Cf. A167411 (minimal K values for the orderly numbers).
Cf. A000005 (tau = number of divisors).
Sequence in context: A177966 A083422 A187581 * A082406 A215938 A352748
KEYWORD
nonn
AUTHOR
Andrew Weimholt, Nov 03 2009
STATUS
approved