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A189506 Irregular triangle read by rows in which row n (n >= 1) lists the base-10 lunar divisors of n.

%I A189506 #31 Nov 16 2018 13:51:43
%S A189506 1,2,3,4,5,6,7,8,9,2,3,4,5,6,7,8,9,3,4,5,6,7,8,9,4,5,6,7,8,9,5,6,7,8,
%T A189506 9,6,7,8,9,7,8,9,8,9,9,1,2,3,4,5,6,7,8,9,10,20,30,40,50,60,70,80,90,1,
%U A189506 2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,31,32,33,34,35,36,37,38,39,41
%N A189506 Irregular triangle read by rows in which row n (n >= 1) lists the base-10 lunar divisors of n.
%H A189506 D. Applegate, M. LeBrun and N. J. A. Sloane, <a href="http://arxiv.org/abs/1107.1130">Dismal Arithmetic</a>, arXiv:1107.1130 [math.NT], 2011. [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
%H A189506 D. Applegate, M. LeBrun, N. J. A. Sloane, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Sloane/carry2.html">Dismal Arithmetic</a>, J. Int. Seq. 14 (2011) # 11.9.8.
%H A189506 <a href="/index/Di#dismal">Index entries for sequences related to dismal (or lunar) arithmetic</a>
%e A189506 The first 11 rows give the divisors of 1 through 11:
%e A189506 1 2 3 4 5 6 7 8 9
%e A189506 2 3 4 5 6 7 8 9
%e A189506 3 4 5 6 7 8 9
%e A189506 4 5 6 7 8 9
%e A189506 5 6 7 8 9
%e A189506 6 7 8 9
%e A189506 7 8 9
%e A189506 8 9
%e A189506 9
%e A189506 1 2 3 4 5 6 7 8 9 10 20 30 40 50 60 70 80 90
%e A189506 1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 17 18 19 21 22 23 24 25 26 27 28 29 31 32 33 34 35 36 37 38 39 41 ... 99 (= all zeroless 1- and 2-digit numbers).
%o A189506 (PARI) A189506_row(n)={my(d=digits(n),m=vecmin(d),c=vector(#d,i,List()),K,t); for(L=1,#d,K=#d-L+1;forvec(v=vector(L,i,[max(m,i==1),9]), L<=K&& listput(c[L],fromdigits(v))&&next; t=fromdigits(v); forstep(i=#c[K],1,-1, A087062(c[K][i],t)==n||next; listput(c[L],t);break)); L>=K&&forstep(i=#c[K],1,-1,t=c[K][i]; forstep(j=#c[L],1,-1,A087062(c[L][j],t)==n&&next(2)); listpop(c[K],i))); Set(concat(c))} \\ _M. F. Hasler_, Nov 15 2018
%Y A189506 Cf. A087062 (lunar product).
%Y A189506 Row n has A087029(n) terms.
%K A189506 nonn,tabf
%O A189506 1,2
%A A189506 _N. J. A. Sloane_, Apr 25 2011
%E A189506 Minor edits by _M. F. Hasler_, Nov 15 2018