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%I #35 Jul 19 2016 16:27:19
%S 5,14,54,264,1560,10920,97440,876960,10263240,112895640,1348827480,
%T 18029171160,264370186080,3806158356000,62703141621120,
%U 1128159304272000,20422064875212000,404757215566704000,8208550091549808000,177650747421074928000
%N Smallest number x such that sum of divisors of x is n!.
%C For n = 1, a(1) = 1; for n = 2, there is no solution.
%D R. K. Guy (1981): Unsolved Problems In Number Theory, B39.
%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
%F a(n) = Min{x; Sigma[x] = n!} = Min{x; A000203(x) = A000142(n)}
%e For n = 6 the 15 solutions are as follows: {264,270,280,354,376,406,418,435,459,478,537,623,649,667,719}
%Y Cf. A000203, A000142, A055486, A055487, A055489
%K nonn
%O 3,1
%A _Labos Elemer_, Jun 28 2000
%E More terms from _Jud McCranie_, Oct 09 2000
%E a(13), a(14) from _Vim Wenders_, Nov 06 2006, Jan 12 2007
%E a(15), a(16) from _Donovan Johnson_, Aug 26 2008, Mar 26 2010
%E a(17)-a(22) from _Max Alekseyev_, Jan 25 2012
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