A087029 Number of lunar divisors of n (unbounded version).

9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 90, 16, 14, 12, 10, 8, 6, 4, 2, 16, 16, 72, 14, 12, 10, 8, 6, 4, 2, 14, 14, 14, 56, 12, 10, 8, 6, 4, 2, 12, 12, 12, 12, 42, 10, 8, 6, 4, 2, 10, 10, 10, 10, 10, 30, 8, 6, 4, 2, 8, 8, 8, 8, 8, 8, 20, 6, 4, 2, 6, 6, 6, 6, 6, 6, 6, 12, 4, 2, 4, 4, 4, 4

Offset

1,1

Comments

Number of d, 1 <= d < infinity, such that there exists an e, 1 <= e < infinity, with d*e = n, where * is lunar multiplication.

Links

D. Applegate, Table of n, a(n) for n = 1..100000

D. Applegate, C program for lunar arithmetic and number theory

D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic, arxiv:1107.1130 [math-NT], July 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.

Brady Haran and N. J. A. Sloane, Primes on the Moon (Lunar Arithmetic), Numberphile video, Nov 2018.

Index entries for sequences related to dismal (or lunar) arithmetic

Example

The 18 divisors of 10 are 1, 2, ..., 9, 10, 20, 30, ..., 90, so a(10) = 18.

Maple

(Uses programs from A087062. This crude program is valid for n <= 99.) dd2 := proc(n) local t1, t2, i, j; t1 := []; for i from 1 to 99 do for j from i to 99 do if dmul(i, j) = n then t1 := [op(t1), i, j]; fi; od; od; t1 := convert(t1, set); t2 := sort(convert(t1, list)); nops(t2); end;

Prog

(PARI) A087029(n)=#A189506_row(n) \\ To be optimized. - M. F. Hasler, Nov 15 2018

Crossrefs

Cf. A087062 (lunar product).

Cf. A087028, A087083, A186443, A186510. See A189506 for the actual divisors.

See A067399 for the base-2 version.

Sequence in context: A269667 A171816 A083824 * A104348 A251984 A298372

Adjacent sequences: A087026 A087027 A087028 * A087030 A087031 A087032

Keyword

nonn,base,look,easy

Author

Marc LeBrun and N. J. A. Sloane, Oct 19 2003

Extensions

More terms from David Applegate, Nov 07 2003

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

Status

approved