Ramanujan's Sum
The sum
 | (1) |
runs through the residues Relatively Prime to 
, which is important in the representation of numbers by thesums of squares. If 
(i.e., and ' are Relatively Prime), then | (2) |
 | (3) |
is the Möbius Function, and for general 
, | (4) |
References
Vardi, I. Computational Recreations in Mathematica. Redwood City, CA: Addison-Wesley, p. 254, 1991.
- Euler's Distribution Theorem
- Euler's Factorization Method
- Euler's Finite Difference Transformation
- Euler's Graeco-Roman Squares Conjecture
- Euler's Homogeneous Function Theorem
- Euler's Hypergeometric Transformations
- Euler's Idoneal Number
- Euler's Machin-Like Formula
- Euler's Pentagonal Number Theorem
- Euler's Phi Function
- Euler's Polygon Division Problem
- Euler's Quadratic Residue Theorem
- Euler Square
- Euler's Rotation Theorem
- Euler's Rule
- Euler's Series Transformation
- Euler's Spiral
- Euler's Sum of Powers Conjecture
- Euler's Theorem
- Euler's Totient Rule
- Euler's Transform
- Euler's Triangle
- Euler Sum
- Euler Totient Function
- Euler Transformation