cp's OEIS Frontend

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

%I A087028 #17 Aug 06 2014 17:14:12
%S A087028 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,
%T A087028 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,
%U A087028 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
%N A087028 Number of bounded (<=n) lunar divisors of n.
%C A087028 Number of d, 1 <= d <= n, such that there exists an e, 1 <= e <= n, with d*e = n, where * is lunar multiplication.
%H A087028 D. Applegate, <a href="/A087028/b087028.txt">Table of n, a(n) for n = 1..100000</a>
%H A087028 D. Applegate, <a href="/A087061/a087061.txt">C program for lunar arithmetic and number theory</a> [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
%H A087028 D. Applegate, M. LeBrun and N. J. A. Sloane, <a href="http://arxiv.org/abs/1107.1130">Dismal Arithmetic</a> [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
%H A087028 <a href="/index/Di#dismal">Index entries for sequences related to dismal (or lunar) arithmetic</a>
%e A087028 The 10 divisors of 10 <= 10 are 1, 2, ..., 9, 10.
%e A087028 a(100) = 19, since the lunar divisors of 100 <= 100 are 1, 2, ..., 9, 10, 20, ..., 90, 100.
%p A087028 (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;
%Y A087028 Cf. A087029, A087082.
%K A087028 nonn,easy,base
%O A087028 1,10
%A A087028 Marc LeBrun and _N. J. A. Sloane_, Oct 19 2003