Numerus defectivus

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

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

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

Exempla:

10 est numerus defectivus, nam 1+2+5 = 8 < 10.
Omnes numeri primi sunt defectivi, cum 1 sit eorum solus divisor, qui summetur (bene observes: numerus $n$ $n$ ipse semper e summa exceptus est).

Si summa divisorum numeri $n$ $n$ uno est minor $n$ $n$ ipso, $n$ $n$ appellatur numerus leviter^? defectivus. Cunctae potentiae numeri 2 sunt leviter defectivae:

Potentia	Summa divisorum
$2^{2}=4$ $2^{2}=4$	$1+2=3$ $1+2=3$
$2^{3}=8$ $2^{3}=8$	$1+2+4=7$ $1+2+4=7$
$2^{4}=16$ $2^{4}=16$	$1+2+4+8=15$ $1+2+4+8=15$
...	...
$2^{n}$ $2^{n}$	$2^{n}-1$ $2^{n}-1$ ^[1]