Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the 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