Solitary Number

Author

Eric W. Weisstein
December 30, 2016

This notebook downloaded from http://mathworld.wolfram.com/notebooks/IntegerSequences/SolitaryNumber.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/SolitaryNumber.html.

©2016 Wolfram Research, Inc. except for portions noted otherwise

Enumeration

known=Select[Range[372],(PrimePowerQ[#]||GCD[#,DivisorSigma[1,#]]==1&)]

A074902

friendly={6,12,24,28,30,40,42,56,60,66,78,80,84,96,102,108,114,120,132,135,138,140,150,168,174,186,200,204,210,222,224,228,234,240,246,252,258,264,270,273,276,280,282,294,300,308,312,318,330,348,354,360,364,366,372};

Complement[Range[372],known,friendly]

Numbers believed but not proved to be solitary:

believed={10,14,15,20,22,26,33,34,38,44,46,51,54,58,62,68,69,70,72,74,76,82,86,87,88,90,91,92,94,95,99,104,105,106};

Numbers presumably proved to be solitary by special techniques:

Complement[Range[109],known,friendly,believed]