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

%I A087029 #32 Nov 24 2018 00:27:35
%S A087029 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 A087029 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 A087029 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 A087029 Number of lunar divisors of n (unbounded version).
%C A087029 Number of d, 1 <= d < infinity, such that there exists an e, 1 <= e < infinity, with d*e = n, where * is lunar multiplication.
%H A087029 D. Applegate, <a href="/A087029/b087029.txt">Table of n, a(n) for n = 1..100000</a>
%H A087029 D. Applegate, <a href="/A087061/a087061.txt">C program for lunar arithmetic and number theory</a>
%H A087029 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 A087029 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 A087029 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 A087029 <a href="/index/Di#dismal">Index entries for sequences related to dismal (or lunar) arithmetic</a>
%e A087029 The 18 divisors of 10 are 1, 2, ..., 9, 10, 20, 30, ..., 90, so a(10) = 18.
%p A087029 (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 A087029 (PARI) A087029(n)=#A189506_row(n) \\ To be optimized. - _M. F. Hasler_, Nov 15 2018
%Y A087029 Cf. A087062 (lunar product).
%Y A087029 Cf. A087028, A087083, A186443, A186510. See A189506 for the actual divisors.
%Y A087029 See A067399 for the base-2 version.
%K A087029 nonn,base,look,easy
%O A087029 1,1
%A A087029 Marc LeBrun and _N. J. A. Sloane_, Oct 19 2003
%E A087029 More terms from _David Applegate_, Nov 07 2003
%E A087029 Minor edits by _M. F. Hasler_, Nov 15 2018