Numerus sociabilis Nexus interni Nexus externi | Bibliographia | Tabula navigationisIndex numerorum sociabilium notorumTabulae extensae numerorum perfectorum, amicabilium atque sociabilium

NumeriTheoria numerorum


Infinitasnumerus naturalisperiodusnumeri perfectinumeri amicabiles







Systemata Numerica Mathematicae


Numeri Elementarii

Naturales Ndisplaystyle mathbb N 0,1,2,3,... sive 1,2,3,...



  • Primi Pdisplaystyle mathbb P 2,3,5,7,11,...

  • Abundantes

  • Amicabiles

  • Compositi

  • Defectivi

  • Perfecti


  • Sociabiles

Integri Zdisplaystyle mathbb Z ...,-2,-1,0,+1,+2,...



  • Pares ...,-2,0,+2,...


  • Impares ...,-3,-1,+1,+3,...

Rationales Qdisplaystyle mathbb Q
Reales Rdisplaystyle mathbb R



  • Irrationales


  • Algebraici


  • Transcendentes

    • Numerus pi π≈3.14159265358979…displaystyle pi approx 3.14159265358979ldots


    • Numerus Euleri e≈2.718281828459045…displaystyle eapprox 2.718281828459045ldots


Complexi Cdisplaystyle mathbb C



  • Numerus imaginarius i=−1displaystyle i=sqrt -1


  • Quaterni Hdisplaystyle mathbb H


  • Octoni Odisplaystyle mathbb O

Infinitas ∞displaystyle infty



Variae radices

  • Radix binaria(2)

  • Radix octalis(8)

  • Radix decimalis(10)

  • Radix sedecimalis(16)

Numerus sociabilis est numerus naturalis n∈Ndisplaystyle nin mathbb N , cuius summae divisorum quondam iterum ndisplaystyle n adaequent, si aliquotiens divisorum summa summae divisorum recentissimae putetur. Numerus putationum summarum divisorum periodus appellatur.


Omnes numeri perfecti sunt numeri sociabiles periodi 1. Omnes numeri amicabiles sunt numeri sociabiles periodi 2.


Exempla:



  • Numerus perfectus 6 est numerus sociabiles periodi 1, nam 1+2+3=6 et tantum semel ratiocinandum est, ut summa divisorum iterum 6 adaequet.


  • Numeri amicabiles 220 et 284 utrique sunt numeri sociabiles periodi 2, nam summa divisorum numeri 220 est 284 ( 1 + 2 + 4 + 5 + 10 + 11 + 20 + 22 + 44 + 55 + 110 = 284) et summa divisorum numeri 284 est 220 (1 + 2 + 4 + 71 + 142 = 220).

  • 1264460 est numerus sociabilis periodi 4, nam:

summa divisorum numeri 1264460 (22 * 5 * 17 * 3719) est:
1 + 2 + 4 + 5 + 10 + 17 + 20 + 34 + 68 + 85 + 170 + 340 + 3719 + 7438 + 14876 + 18595 + 37190 + 63223 + 74380 + 126446 + 252892 + 316115 + 632230 = 1547860
summa divisorum numeri 1547860 (22 * 5 * 193 * 401) est:
1 + 2 + 4 + 5 + 10 + 20 + 193 + 386 + 401 + 772 + 802 + 965 + 1604 + 1930 + 2005 + 3860 + 4010 + 8020 + 77393 + 154786 + 309572 + 386965 + 773930 = 1727636
summa divisorum numeri 1727636 (22 * 521 * 829) est:
1 + 2 + 4 + 521 + 829 + 1042 + 1658 + 2084 + 3316 + 431909 + 863818 = 1305184
summa divisorum numeri 1305184 (25 * 40787) est:
1 + 2 + 4 + 8 + 16 + 32 + 40787 + 81574 + 163148 + 326296 + 652592 = 1264460.

Nexus interni


  • Numerus perfectus

  • Numeri amicabiles


Nexus externi |


  • Index numerorum sociabilium notorum

  • Tabulae extensae numerorum perfectorum, amicabilium atque sociabilium


Bibliographia |


  • P. Poulet, #4865, L'intermediare des math. 25 (1918), pp. 100-101.

  • H. Cohen, On amicable and sociable numbers, Math. Comp. 24 (1970), pp. 423-429


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