A087029 - OEIS

%I #32 Nov 24 2018 00:27:35

%S 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,

%T 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,

%U 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

%N Number of lunar divisors of n (unbounded version).

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

%H D. Applegate, <a href="/A087029/b087029.txt">Table of n, a(n) for n = 1..100000</a>

%H D. Applegate, <a href="/A087061/a087061.txt">C program for lunar arithmetic and number theory</a>

%H D. Applegate, M. LeBrun and N. J. A. Sloane, <a href="http://arxiv.org/abs/1107.1130">Dismal Arithmetic</a>, 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]

%H D. Applegate, M. LeBrun, N. J. A. Sloane, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Sloane/carry2.html">Dismal Arithmetic</a>, J. Int. Seq. 14 (2011) # 11.9.8.

%H Brady Haran and N. J. A. Sloane, <a href="https://youtu.be/cZkGeR9CWbk">Primes on the Moon (Lunar Arithmetic)</a>, Numberphile video, Nov 2018.

%H <a href="/index/Di#dismal">Index entries for sequences related to dismal (or lunar) arithmetic</a>

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

%p (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;

%o (PARI) A087029(n)=#A189506_row(n) \\ To be optimized. - _M. F. Hasler_, Nov 15 2018

%Y Cf. A087062 (lunar product).

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

%Y See A067399 for the base-2 version.

%K nonn,base,look,easy

%O 1,1

%A Marc LeBrun and _N. J. A. Sloane_, Oct 19 2003

%E More terms from _David Applegate_, Nov 07 2003

%E Minor edits by _M. F. Hasler_, Nov 15 2018