Loading docs/math/mobius.md +1 −1 Original line number Diff line number Diff line Loading @@ -926,7 +926,7 @@ $$ &&\sum_{d=1}^{n}d^3\sum_{t=1}^{\lfloor\frac{n}{d}\rfloor}t^2 \mu(t)\sum_{i=1}^{\lfloor\frac{n}{td}\rfloor}\sum_{j=1}^{\lfloor\frac{n}{td}\rfloor}ij\\ &=&\sum_{d=1}^{n}d^3\sum_{t=1}^{\lfloor\frac{n}{d}\rfloor}t^2 \mu(t)\cdot F^2\left(\left\lfloor\frac{n}{td}\right\rfloor\right)\\ &=&\sum_{T=1}^{n}F^2\left(\left\lfloor\frac{n}{T}\right\rfloor\right) \sum_{d\mid T}d^3\left(\frac{T}{d}\right)^2\mu\left(\frac{T}{d}\right)\\ &=&\sum_{T=1}^{n}F^2\left(\left\lfloor\frac{n}{T}\right\rfloor\right) T^2\sum_{d\mid T}d\cdot\mu(\dfrac{T}{d}) &=&\sum_{T=1}^{n}F^2\left(\left\lfloor\frac{n}{T}\right\rfloor\right) T^2\sum_{d\mid T}d\cdot\mu\left(\dfrac{T}{d}\right) \end{aligned} $$ Loading Loading
docs/math/mobius.md +1 −1 Original line number Diff line number Diff line Loading @@ -926,7 +926,7 @@ $$ &&\sum_{d=1}^{n}d^3\sum_{t=1}^{\lfloor\frac{n}{d}\rfloor}t^2 \mu(t)\sum_{i=1}^{\lfloor\frac{n}{td}\rfloor}\sum_{j=1}^{\lfloor\frac{n}{td}\rfloor}ij\\ &=&\sum_{d=1}^{n}d^3\sum_{t=1}^{\lfloor\frac{n}{d}\rfloor}t^2 \mu(t)\cdot F^2\left(\left\lfloor\frac{n}{td}\right\rfloor\right)\\ &=&\sum_{T=1}^{n}F^2\left(\left\lfloor\frac{n}{T}\right\rfloor\right) \sum_{d\mid T}d^3\left(\frac{T}{d}\right)^2\mu\left(\frac{T}{d}\right)\\ &=&\sum_{T=1}^{n}F^2\left(\left\lfloor\frac{n}{T}\right\rfloor\right) T^2\sum_{d\mid T}d\cdot\mu(\dfrac{T}{d}) &=&\sum_{T=1}^{n}F^2\left(\left\lfloor\frac{n}{T}\right\rfloor\right) T^2\sum_{d\mid T}d\cdot\mu\left(\dfrac{T}{d}\right) \end{aligned} $$ Loading