

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
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OFFSET

1,2


COMMENTS

The very orderly numbers are orderly numbers (Cf. A167408) with K = tau(N)+1


LINKS

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


MATHEMATICA

veryOrderlyQ[n_] := (If[tau = DivisorSigma[0, n]; Union[Mod[Divisors[n], tau + 1]] == Range[tau], Return[True]]; False); Select[ Range[260], veryOrderlyQ] (* JeanFrançois Alcover, Aug 19 2013 *)


PROG

(PARI)
vo(n)=#(n=divisors(n))==#(n=Set(n%(1+#n))) & n[1]!="0"
for(n=1, 999, vo(n)&print1(n", ")) \\ M. F. Hasler


CROSSREFS

Cf. A167408  Orderly Numbers
Cf. A167410  Disorderly Numbers  numbers not in A167408
Cf. A167411  Minimal K Values for the Orderly Numbers
Sequence in context: A177966 A083422 A187581 * A082406 A215938 A352748
Adjacent sequences: A167406 A167407 A167408 * A167410 A167411 A167412


KEYWORD

nonn


AUTHOR

Andrew Weimholt, Nov 03 2009


STATUS

approved



