Fòmil pou nonm konpoze

Nonm konpoze yo lye ak nosyon nonm premye .

Definisyon

Yon antye natirèl n se yon konpoze si e sèlman si li pi gran ke 1 e ke li pa yon nonm premye.

An nou note $𝕏_{n}$ nonm konpoze rang n e $(𝕏_{n})$ swit kwasant nonm konpoze yo.

$\forall n \in ℕ^{*}$

1 - [\frac{[\frac{(n - 1)! + 1}{n}]}{\frac{(n - 1)! + 1}{n}}] = 1 ⟺ n \in 𝕏

$1 - [\frac{[\frac{(n - 1)! + 1}{n}]}{\frac{(n - 1)! + 1}{n}}] = 0 ⟺ n \notin 𝕏$

fonksyon karakteristik si nou dezye pa $φ$ nou genyen :

$φ (n) = 1 - [\frac{[\frac{(n - 1)! + 1}{n}]}{\frac{(n - 1)! + 1}{n}}]$

$φ (n) = ([\frac{[\frac{{(n!)}^{2}}{n^{3}}]}{\frac{{(n!)}^{2}}{n^{3}}}] - [\frac{1}{n}])$

$𝕏_{n} = \sum_{i = 1}^{4 m} ([\frac{1 + \sum_{m = 1}^{i} φ (m)}{n + 1}] \times [\frac{n + 1}{1 + \sum_{m = 1}^{i} φ (m)}] \times i \times φ (i))$

$𝕏_{n} = \sum_{i = 1}^{2 m + 2} ([\frac{1 + \sum_{m = 1}^{i} φ (m)}{n + 1}] \times [\frac{n + 1}{1 + \sum_{m = 1}^{i} φ (m)}] \times i \times φ (i))$