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

0,1

Comments

Does a(n) exist for every n?

Links

Table of n, a(n) for n=0..17.

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

Example

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.

Mathematica

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

Crossrefs

Cf. A001157, A007368.

Sequence in context: A109347 A054210 A225778 * A092650 A353586 A363381

Adjacent sequences: A271439 A271440 A271441 * A271443 A271444 A271445

Keyword

nonn

Author

Giovanni Resta, Apr 20 2016

Status

approved