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

1,2

Links

Table of n, a(n) for n=1..100.

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

Example

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).

Prog

(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

Crossrefs

Cf. A087062 (lunar product).

Row n has A087029(n) terms.

Sequence in context: A238986 A227876 A276716 * A173529 A273005 A093017

Adjacent sequences: A189503 A189504 A189505 * A189507 A189508 A189509

Keyword

nonn,tabf

Author

N. J. A. Sloane, Apr 25 2011

Extensions

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

Status

approved