&[1]\displaystyle\sum_{k=1}^{n}k=\frac{1}{2}n(n+1)\\ &[2] \displaystyle\sum_{k=1}^{n}k^2=\frac{1}{6}n(n+1)(2n+1)\\ &[3] \displaystyle\sum_{k=1}^{n}k^3=\Big\{\frac{1 ...

Abstract Denote by τ k (n), ω (n) and μ 2 (n) the number of representations of n as a product of k natural numbers, the number of distinct prime factors of n and the characteristic function of the ...

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