Sum of Squares Function -- from Wolfram MathWorld

The number of representations of n by k squares, allowing zeros and distinguishing signs and order, is denoted r_k(n). The special case k=2 corresponding to two squares is often denoted simply r_2(n)=r(n) (e.g., Hardy and Wright 1979, p. 241; Shanks 1993, p. 162). For example, consider the number of ways of representing 5 as the sum of two squares: 5 = (-2)^2+(-1)^2 (1) = (-2)^2+1^2 (2) = 2^2+(-1)^2 (3) = 2^2+1^2 (4) = (-1)^2+(-2)^2 (5) = (-1)^2+2^2 (6) = 1^2+(-2)^2 (7) =

Jacobi Theta Functions -- from Wolfram MathWorld

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Sum of Squares Function -- from Wolfram MathWorld

Sum of Squares Function -- from Wolfram MathWorld

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Divisor Function -- from Wolfram MathWorld

Sum of Squares Function -- from Wolfram MathWorld

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Sum of Squares Function -- from Wolfram MathWorld

Divisor Function -- from Wolfram MathWorld