A271442 - OEIS

A271442

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.

%I #6 Apr 20 2016 09:21:47

%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