A110077 - OEIS

%I #25 Mar 04 2018 03:12:02

%S 1,0,0,0,8743,71193,640737,5906061,65624979,590624811,5498542791,

%T 55995364341,549871699041,5582882097891,55828827410391,

%U 542546715730761,5469955867029591,53226216007355979,532262221390168479,5300249369031696429,52602977416561263909,531074469279114815229

%N a(n) is the smallest number m such that sigma(m)=10^n and if there is no such m, a(n)=0.

%C A110078(n) gives number of solutions of the equation sigma(x)=10^n.

%C Conjecture: For n>3 a(n) is positive.

%H Max Alekseyev, <a href="/A110077/b110077.txt">Table of n, a(n) for n = 0..1000</a>

%H Max Alekseyev, <a href="http://home.gwu.edu/~maxal/gpscripts/">PARI/GP scripts for miscellaneous math problems</a>

%H 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 a(9)=590624811 because sigma(590624811)=sigma(3^3*7*3124999) sigma(3^3)*sigma(7)*sigma(3124999)=40*8*3125000=10^9 and 590624811 is the smallest number m with this property (sigma(m)=10^9).

%o (PARI) { a(n) = invsigma(10^n)[1] } \\ _Max Alekseyev_, Apr 26 2010

%Y Cf. A110076, A110078.

%K nonn

%O 0,5

%A _Farideh Firoozbakht_, Aug 01 2005

%E a(10)-a(11) from _Donovan Johnson_ and _Farideh Firoozbakht_, Nov 22 2008

%E a(12) onward from _Max Alekseyev_, Apr 26 2010, Mar 06 2014