

A087029


Number of lunar divisors of n (unbounded version).


11



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
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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, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic, arxiv:1107.1130 [mathNT], 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.


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



CROSSREFS

See A067399 for the base2 version.


KEYWORD



AUTHOR



EXTENSIONS



STATUS

approved



