Numerus abundans

Systemata Numerica Mathematicae

Numeri Elementarii
Naturales $\mathbb {N}$ {0,1,2,3,...} sive {1,2,3,...} Primi $\mathbb {P}$ {2,3,5,7,11,...} Abundantes Amicabiles Compositi Defectivi Perfecti Sociabiles Integri $\mathbb {Z}$ {...,-2,-1,0,+1,+2,...} Pares {...,-2,0,+2,...} Impares {...,-3,-1,+1,+3,...} Rationales $\mathbb {Q}$ Reales $\mathbb {R}$ Irrationales Complexi ℂ Algebraici Transcendentes Numerus pi $\pi =3.14159265358979\ldots$ Numerus Euleri $e=2.718281828459045\ldots$ Numerus imaginarius $i={\sqrt {-1}}$ Quaterni $\mathbb {H}$ Octoni $\mathbb {O}$ Infinitas $\infty$
Variae radices
Radix binaria(2) Radix octalis(8) Radix decimalis(10) Radix sedecimalis(16)

Numerus abundans est numerus $n$, cuius summa divisorum maior numero $n$ ipso - e summa excepto - est. Vel symbolis mathematicis expressum

$\sum _{d|n,d\not =n}d>n$.

Exempla:

• Numerus abundans par minimus est 12 (1+2+3+4+6 = 16 > 12). Sequentes numeri abundantes pares sunt:

12, 18, 20, 24, 30, 36, 40, 42, …

• Numerus abundans impar minimus est 945 (1+3+5+7+9+15+21+27+35+45+63+105+135 +189+315 = 975 > 945). Sequentes numeri abundantes impares sunt:

945, 1575, 2205, 2835, 3465, 4095, 4725, 5355, 5775, …

Nexus interni

• Numerus perfectus
• Numerus defectivus