Unitary Divisor Function

Author

Eric W. Weisstein
February 23, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/NumberTheory/UnitaryDivisorFunction.nb.

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

©2005 Wolfram Research, Inc. except for portions noted otherwise

Enumeration

Table

(data=Table[UnitaryDivisorSigma[k,#]&/@Range[20],{k,0,4}])//ColumnForm

<<Utilities`Plot`

Show[GraphicsArray[Partition[Block[{$DisplayFunction=Identity},MapIndexed[IntegerListPlot[#1,AxesLabel->TraditionalForm/@{n,(Subscript[σ, #2[[1]]-1]^("*"))}]&,data]],2]]]

Check

u=UnitaryDivisors/@Range[2,20]

UnitaryDivisorSigma[1,#]&/@Range[2,20]

Plus@@@u

UnitaryDivisorSigma[2,#]&/@Range[2,20]

Plus@@@(u^2)

UnitaryDivisorSigma[3,#]&/@Range[2,20]

Plus@@@(u^3)