

A123523


Smallest odd number k such that sigma(x)=k has exactly n solutions.


1



1, 31, 347529, 10773399, 4104665019, 77253471477, 28732655133, 35492068813383, 108695634368139, 461396894573979, 68452476460273269, 2529134502772059, 99414440839732473
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OFFSET

1,2


COMMENTS

Note that sigma(x) is odd iff x is in A028982 (numbers of the form m^2 or 2m^2 for m>0).
a(14) > 10^18. a(15) = 175792216832685999. a(16) > 10^18.  Donovan Johnson, Jun 09 2011


LINKS

Table of n, a(n) for n=1..13.


EXAMPLE

For n=3, sigma(x)=347529 has solutions x = 164836, 203522, 239121.


MATHEMATICA

Needs["Statistics`DataManipulation`"]; nn=10^6; t1=DivisorSigma[1, Range[nn]^2]; t2=DivisorSigma[1, 2*Range[nn/Sqrt[2]]^2]; t=Join[t1, t2]; {u, v}=Transpose[Sort[Frequencies[t]]]; Table[p=Position[u, i, 1, 1][[1, 1]]; v[[p]], {i, Length[Union[u]]}]


CROSSREFS

Different from A123524.
Sequence in context: A059113 A057839 A123524 * A079595 A051155 A216791
Adjacent sequences: A123520 A123521 A123522 * A123524 A123525 A123526


KEYWORD

more,nonn


AUTHOR

T. D. Noe, Oct 02 2006


EXTENSIONS

35492068813383 from Martin Fuller, Oct 07 2006
a(9)a(10) from Donovan Johnson, Dec 09 2008
a(11)a(13) from Donovan Johnson, Jun 09 2011


STATUS

approved



