%I
%S 2,1,50,22100,6409000,32045000,1185665000,11856650000,628402450000,
%T 1169065690000,16338463700000,81692318500000,875993015300000,
%U 1388769414500000,8054862604100000,88701519427300000,443507597136500000,80548626041000000
%N a(n) is the smallest k such that sigma(2,x) = k has exactly n solutions, where sigma(2,x) is the sum of the squares of the divisors of x.
%C Does a(n) exist for every n?
%H Giovanni Resta, <a href="/A271442/a271442.txt">Table of solutions corresponding to a(n), for n=0..17</a>
%e a(3) = 22100 because there are exactly 3 values x (120, 130, and 141) such that sigma(2,x) = 22100, and this property does not hold for any number smaller than 22100.
%t t=Gather@ Sort@ DivisorSigma[2, Range@ 800000]; Join[{2}, Table[ Select[t, k == Length@ # &, 1][[1, 1]], {k, 8}]]
%Y Cf. A001157, A007368.
%K nonn
%O 0,1
%A _Giovanni Resta_, Apr 20 2016
