A087028 Number of bounded (<=n) lunar divisors of n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 10, 9, 8, 7, 6, 5, 4, 3, 2, 9, 9, 9, 8, 7, 6, 5, 4, 3, 2, 8, 8, 8, 8, 7, 6, 5, 4, 3, 2, 7, 7, 7, 7, 7, 6, 5, 4, 3, 2, 6, 6, 6, 6, 6, 6, 5, 4, 3, 2, 5, 5, 5, 5, 5, 5, 5, 4, 3, 2, 4, 4, 4, 4, 4, 4, 4, 4, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 19, 10, 9, 8, 7, 6, 5, 4, 3, 2, 100, 91, 17, 15, 13, 11, 9, 7, 5, 3, 25, 25, 81, 22, 19, 16, 13, 10, 7, 4, 22, 22, 22, 64, 19, 16, 13, 10, 7, 4, 19, 19, 19, 19, 49, 16, 13, 10, 7, 4, 16, 16, 16, 16, 16, 36, 13, 10, 7, 4, 13, 13, 13, 13, 13, 13, 25, 10, 7, 4, 10, 10, 10, 10, 10, 10, 10, 16, 7, 4, 7, 7, 7, 7, 7, 7, 7, 7, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 17

Offset

1,10

Comments

Number of d, 1 <= d <= n, such that there exists an e, 1 <= e <= n, 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 [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]

D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]

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

Example

The 10 divisors of 10 <= 10 are 1, 2, ..., 9, 10.
a(100) = 19, since the lunar divisors of 100 <= 100 are 1, 2, ..., 9, 10, 20, ..., 90, 100.

Maple

(Uses programs from A087062) dd1 := proc(n) local t1, t2, i, j; t1 := []; for i from 1 to n do for j from i to n 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;

Crossrefs

Cf. A087029, A087082.

Sequence in context: A112120 A099401 A263450 * A145279 A103708 A239051

Adjacent sequences: A087025 A087026 A087027 * A087029 A087030 A087031

Keyword

nonn,easy,base

Author

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

Status

approved