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

Author

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

Keywords

• nonn
• easy
• base

Comments

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

Examples

			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.
		

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

Crossrefs

Cf. A087029, A087082.

Programs

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;