A169982 - OEIS

%I #14 Aug 06 2014 16:23:20

%S 1,2,4,14,41,222

%N Maximal number of lunar divisors of any 9-ish number with n digits.

%H D. Applegate, M. LeBrun and N. J. A. Sloane, <a href="http://arxiv.org/abs/1107.1130">Dismal Arithmetic</a> [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]

%H <a href="/index/Di#dismal">Index entries for sequences related to dismal (or lunar) arithmetic</a>

%e At length 1, 9 has one divisor, 9 itself.

%e At length 2, all 18 9-ish numbers N are lunar primes and therefore have two divisors, 9 and N.

%e At length 3, 998 and many others have 4 divisors.

%e At length 4, just 4 numbers have 14 divisors, namely 9988, 8988, 8899, 8898.

%e At length 5, there is a unique number with 41 divisors, 88988.

%e At length 9, there is a unique number with 222 divisors, 99999.

%Y Cf. A169983 (which is a lower bound).

%K nonn,base,more

%O 1,2

%A _David Applegate_, _Marc LeBrun_ and _N. J. A. Sloane_, Aug 21 2010