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.

2, 1, 50, 22100, 6409000, 32045000, 1185665000, 11856650000, 628402450000, 1169065690000, 16338463700000, 81692318500000, 875993015300000, 1388769414500000, 8054862604100000, 88701519427300000, 443507597136500000, 80548626041000000

Offset: 0

Author

Giovanni Resta, Apr 20 2016

Keywords

• nonn

Comments

Does a(n) exist for every n?

Examples

			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.
		

Links

• Giovanni Resta, Table of solutions corresponding to a(n), for n=0..17

Crossrefs

Cf. A001157, A007368.

Programs

Mathematica

t=Gather@ Sort@ DivisorSigma[2, Range@ 800000]; Join[{2}, Table[ Select[t, k == Length@ # &, 1][[1, 1]], {k, 8}]]