Even Divisor Function

Author

Eric W. Weisstein
September 1, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/NumberTheoreticFunctions/EvenDivisorFunction.nb.

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

©2008 Wolfram Research, Inc. except for portions noted otherwise

Sums

DivisorSum[n,((#1)^k)&,EvenQ[#1]&]==If[EvenQ[n],(2^k) (DivisorSigma[k, (n/2)]),0]

DivisorSum[n,#^2&,EvenQ[#]&]

Table[DivisorSum[n,#^k&,EvenQ[#]&],{k,4}]

Subtract@@@Flatten[Table[{DivisorSum[n,((#)^k)&,EvenQ[#]&],If[EvenQ[n],(2^k)DivisorSigma[k,n/2],0]},{k,5},{n,100}],1]//Union

Tables

Table[DivisorSigmaEven[0,n],{n,2,20,2}]

Table[DivisorSigma[0,n],{n,1,10}]

Table[DivisorSigmaEven[1,n],{n,2,20,2}]/2

Table[DivisorSigma[1,n],{n,10}]

Table[DivisorSigmaEven[2,n],{n,2,20,2}]/4

Table[DivisorSigma[2,n],{n,10}]

Table[DivisorSigmaEven[3,n],{n,2,20,2}]

Table[2^3DivisorSigma[3,n/2],{n,2,20,2}]

Table[DivisorSigma[3,n],{n,10}]