A190876 Numbers 1 through 8 together with numbers congruent to 9 mod 10.

1, 2, 3, 4, 5, 6, 7, 8, 9, 19, 29, 39, 49, 59, 69, 79, 89, 99, 109, 119, 129, 139, 149, 159, 169, 179, 189, 199, 209, 219, 229, 239, 249, 259, 269, 279, 289, 299, 309, 319, 329, 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

Offset: 1

Author

N. J. A. Sloane, May 23 2011

Keywords

• nonn
• base
• easy

Comments

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• 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
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A017377.

Programs

Magma

[n lt 9 select n else 10*n-81: n in [1..70]]; // Bruno Berselli, May 24 2011

Mathematica

CoefficientList[Series[x*(1+9*x^9)/(1-x)^2,{x,0,69}],x] (* Stefano Spezia, May 26 2025 *)

Maxima

makelist(if n<9 then n else 10*n-81,n,1,70); /* Bruno Berselli, May 24 2011 */

Formula

G.f.: x*(1+9*x^9)/(1-x)^2. - Bruno Berselli, May 23 2011

a(n) = 2*a(n-1) -a(n-2). - Vincenzo Librandi, Jul 12 2012