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%I #28 Sep 08 2022 08:44:56
%S 1,18,217,2340,24211,246078,2480437,24902280,249511591,2497558338,
%T 24987792457,249938963820,2499694822171,24998474116998,
%U 249992370597277,2499961853010960,24999809265103951,249999046325618058,2499995231628286897
%N Sum of divisors of 10^n.
%C A072692(n) = A049000(n) + a(n).
%C a(n) is the number of full-dimensional lattices in Z^(n+1) with volume 10. - _Álvar Ibeas_, Nov 29 2015
%H Vincenzo Librandi, <a href="/A046915/b046915.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (18,-97,180,-100).
%F 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
%F a(n) = 18*a(n-1)-97*a(n-2)+180*a(n-3)-100*a(n-4). - _Colin Barker_, Jan 27 2015
%F G.f.: -(10*x^2-1) / ((x-1)*(2*x-1)*(5*x-1)*(10*x-1)). - _Colin Barker_, Jan 27 2015
%e At 10^1 the factors are 1, 2, 5, 10. The sum of these factors is 18: 1 + 2 + 5 + 10.
%t Table[DivisorSigma[1, 10^n], {n, 0, 18}] (* _Jayanta Basu_, Jun 30 2013 *)
%o (Magma) [1/4*(2^(n+1)-1)*(5^(n+1)-1): n in [0..20]]; // _Vincenzo Librandi_, Oct 03 2011
%o (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
%o (PARI) a(n) = sigma(10^n); \\ _Altug Alkan_, Dec 04 2015
%Y Cf. A000203 (sigma(n)), A049000, A072692. 10th row of A160870, shifted.
%K easy,nonn
%O 0,2
%A _Enoch Haga_
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