A190876 - OEIS

%I #30 Mar 17 2023 11:05:20

%S 1,2,3,4,5,6,7,8,9,19,29,39,49,59,69,79,89,99,109,119,129,139,149,159,

%T 169,179,189,199,209,219,229,239,249,259,269,279,289,299,309,319,329,

%U 339,349,359,369,379,389,399,409,419,429,439,449,459,469,479,489,499,509,519,529,539,549,559,569,579,589,599,609

%N Numbers 1 through 8 together with numbers congruent to 9 mod 10.

%C In lunar arithmetic, numbers n with the property that the sum of the divisors of n that are <= n is equal to n.

%H Vincenzo Librandi, <a href="/A190876/b190876.txt">Table of n, a(n) for n = 1..1000</a>

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

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F G.f.: x*(1+9*x^9)/(1-x)^2. - _Bruno Berselli_, May 23 2011

%F a(n) = 2*a(n-1) -a(n-2). - _Vincenzo Librandi_, Jul 12 2012

%o (Maxima) makelist(if n<9 then n else 10*n-81,n,1,70); /* _Bruno Berselli_, May 24 2011 */

%o (Magma) [n lt 9 select n else 10*n-81: n in [1..70]]; // _Bruno Berselli_, May 24 2011

%Y Cf. A017377.

%K nonn,base

%O 1,2

%A _N. J. A. Sloane_, May 23 2011