Număr sfenic

Număr sfenic
Nr. presupus de termeniinfinit
Formulaprodusul a trei numere prime distincte
Primii termeni30, 42, 66, 70, 78, 102, 105, 110, 114, 130, 138, 154, 165, 170, 174, 182, 186, 190, 195, 222, 230
Cel mai mare termen cunoscut(282,589,933 − 1) × (277,232,917 − 1) × (274,207,281 − 1)[1]
Index OEIS

În matematică, un număr sfenic (în engleză sphenic number; din limba greacă veche σφήνα) este un număr întreg pozitiv, liber de pătrate, ce are trei factori primi.[2] Este produsul a trei numere prime distincte. Cel mai mare astfel de număr cunoscut este produsul celor mai mari trei numere prime cunoscute.[3]

30 = 2 × 3 × 5; 30 este cel mai mic număr sfenic, produsul celor mai mici trei numere prime.

30 are o sumă alicotă (aliquot sum) de 42; al doilea număr sfenic (42) și toate numerele sfenice de forma 2 × 3 × r, unde r este un număr prim mai mare decât 3, au o sumă alicotă cu 12 mai mare decât ele.[4]

Primele numere sfenice sunt:

30, 42, 66, 70, 78, 102, 105, 110, 114, 130, 138, 154, 165, 170, 174, 182, 186, 190, 195, 222, 230, 231, 238, 246, 255, 258, 266, 273, 282, 285, 286, 290, 310, 318, 322, 345, 354, 357, 366, 370, 374, 385, 399, 402, 406, 410, 418, 426, 429, 430, 434, 435, 438

Toate numerele sfenice sunt prin definiție libere de pătrat, deoarece factorii primi trebuie să fie distincți. Funcția Möbius a oricărui număr sfenic este -1.

Note

  1. ^ Cel mai mare termen cunoscut, primes.utm.edu
  2. ^ Marius Coman, Enciclopedia matematică a claselor de numere întregi
  3. ^ Șirul A007304 la Enciclopedia electronică a șirurilor de numere întregi (OEIS)
  4. ^ suma alicotă s(n) a unui număr întreg pozitiv n este suma tuturor divizorilor proprii ai lui n, adică a tuturor divizorilor lui n, în afară de n însuși.

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