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A110076 a(n) is the largest number m such that sigma(m)=10^n, or if there is no such m a(n)=0.

%I A110076 #16 Jul 19 2016 16:22:30
%S A110076 1,0,0,0,9481,99301,997501,9993001,99948001,999795001,9999750001,
%T A110076 99998670001,999997950001,9999986700001,99999975000001,
%U A110076 999999198750001,9999999187500001,99999995096707501,999999919987500001,9999999986700000001,99999499999999800001,999999999907500000001,9999999999796009687501
%N A110076 a(n) is the largest number m such that sigma(m)=10^n, or if there is no such m a(n)=0.
%C A110076 Conjecture: For n>3 a(n) is positive.
%C A110076 For 4 <= n <= 102, a(n) is the product of two distinct primes, but a(103) = a(49)*a(54) and is the product of four distinct primes: 1862645149230957031249999 * 5368709119999999999999999 * 79999999999999999999999999 * 12499999999999999999999999999. - _David Wasserman_, Nov 18 2008
%H A110076 Max Alekseyev, <a href="/A110076/b110076.txt">Table of n, a(n) for n = 0..1000</a>
%H A110076 Max A. Alekseyev, <a href="https://www.emis.de/journals/JIS/VOL19/Alekseyev/alek5.html">Computing the Inverses, their Power Sums, and Extrema for Euler's Totient and Other Multiplicative Functions</a>. Journal of Integer Sequences, Vol. 19 (2016), Article 16.5.2
%e A110076 a(12)=999997950001 because sigma(999997950001)=sigma(799999*1249999) =800000*1250000=10^12 and 999997950001 is the largest number with this property(sigma(m)=10^12).
%t A110076 a[0] = 1; a[1] = a[2] = a[3] = 0; a[n_] := (For[m = 1, DivisorSigma[ 1, 10^n - m] != 10^n, m++ ];10^n - m); Do[Print[a[n]], {n, 0, 12}]
%Y A110076 Cf. A110077, A110078.
%K A110076 nonn
%O A110076 0,5
%A A110076 _Farideh Firoozbakht_, Jul 31 2005
%E A110076 More terms from _David Wasserman_, Nov 18 2008
%E A110076 Terms a(19) onward from _Max Alekseyev_, Mar 06 2014