

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.


1



2, 1, 50, 22100, 6409000, 32045000, 1185665000, 11856650000, 628402450000, 1169065690000, 16338463700000, 81692318500000, 875993015300000, 1388769414500000, 8054862604100000, 88701519427300000, 443507597136500000, 80548626041000000
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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 A221194 A309207
Adjacent sequences: A271439 A271440 A271441 * A271443 A271444 A271445


KEYWORD

nonn


AUTHOR

Giovanni Resta, Apr 20 2016


STATUS

approved



