A173569 - OEIS

%I #7 Aug 28 2013 10:16:30

%S 1,3,8,15,24,36,48,72,96,140,120,180,280,240,336,420,360,480,672,864,

%T 900,720,840,1008,1080,1260,1980,1440,2340,1680,3744,2160,3024,2880,

%U 4032,2520,3780,3360,4680,4320,6048,9450,9072,6300,7200,6720,5040,8640

%N Least number k such that the function described in A137921 equals n.

%H Robert G. Wilson v, <a href="/A173569/b173569.txt">Table of n, a(n) for n = 1..2665 </a>.

%t f[n_] := Length@ Split[ Divisors@n, #2 - #1 == 1 &] (* f(n) from Dr. Bobby R. Treat *); t = Table[0, {100}]; k = 1; While[k < 10^9, a = f@k; If[a < 101 && t[[a]] == 0, t[[a]] = k; Print[{k, a}]]; k++ ]; t

%Y Cf. A137921, A173570.

%Y Cf. A137921: a(n) = number of "divisor islands" of n. A divisor island is any set of consecutive divisors of a number where no pairs of consecutive divisors in the set are separated by 2 or more. [From _Robert G. Wilson v_, May 20 2010]

%K nonn

%O 1,2

%A _Robert G. Wilson v_, Feb 22 2010