A046915 Sum of divisors of 10^n.

1, 18, 217, 2340, 24211, 246078, 2480437, 24902280, 249511591, 2497558338, 24987792457, 249938963820, 2499694822171, 24998474116998, 249992370597277, 2499961853010960, 24999809265103951, 249999046325618058, 2499995231628286897

Offset

0,2

Comments

A072692(n) = A049000(n) + a(n).

a(n) is the number of full-dimensional lattices in Z^(n+1) with volume 10. - Álvar Ibeas, Nov 29 2015

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (18,-97,180,-100).

Formula

a(n) = 1/4*(2^(n+1)-1)*(5^(n+1)-1). E.g., a(1) = 1/4*(2^2-1)*(5^2-1) = 18. - Vladeta Jovovic, Dec 18 2001

a(n) = 18*a(n-1)-97*a(n-2)+180*a(n-3)-100*a(n-4). - Colin Barker, Jan 27 2015

G.f.: -(10*x^2-1) / ((x-1)*(2*x-1)*(5*x-1)*(10*x-1)). - Colin Barker, Jan 27 2015

Example

At 10^1 the factors are 1, 2, 5, 10. The sum of these factors is 18: 1 + 2 + 5 + 10.

Mathematica

Table[DivisorSigma[1, 10^n], {n, 0, 18}] (* Jayanta Basu, Jun 30 2013 *)

Prog

(Magma) [1/4*(2^(n+1)-1)*(5^(n+1)-1): n in [0..20]]; // Vincenzo Librandi, Oct 03 2011
(PARI) Vec(-(10*x^2-1)/((x-1)*(2*x-1)*(5*x-1)*(10*x-1)) + O(x^100)) \\ Colin Barker, Jan 27 2015
(PARI) a(n) = sigma(10^n); \\ Altug Alkan, Dec 04 2015

Crossrefs

Cf. A000203 (sigma(n)), A049000, A072692. 10th row of A160870, shifted.

Sequence in context: A019757 A021503 A025470 * A041616 A224296 A019333

Adjacent sequences: A046912 A046913 A046914 * A046916 A046917 A046918

Keyword

easy,nonn

Author

Enoch Haga

Status

approved