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

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, 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, 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

Offset: 1

Author

N. J. A. Sloane, Apr 25 2011

Keywords

• nonn
• tabf

Examples

			The first 11 rows give the divisors of 1 through 11:
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 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 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).
		

Links

• D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic, 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]
• D. Applegate, M. LeBrun, N. J. A. Sloane, Dismal Arithmetic, J. Int. Seq. 14 (2011) # 11.9.8.
• Index entries for sequences related to dismal (or lunar) arithmetic

Crossrefs

Cf. A087062 (lunar product).

Row n has A087029(n) terms.

Programs

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

Extensions

Minor edits by M. F. Hasler, Nov 15 2018