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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 1 20:14 EDT 2014. Contains 247522 sequences.