Número de Knödel

Donat un número natural n, un número de Knödel és un número compuesto m en la propietat de que cada i < m coprimo en m satisfà $i^{m-n}\equiv 1(\mathrm{mod}m)$.

El conjunt de tots els número natural donat n es denomina el conjunt dels números de Knödel K_n. Note's que K₁ són els números de Carmichael.

Eixemples

Estos són els primers números de Knödel K_n per a 0 < n < 26.:

n	Kn	OEIS
1	561, 1105, 1729, 2465, 2821, 6601, 8911, 10585, 15841, 29341, 41041, 46657, 52633, 62745, 63973, 75361, 101101, 115921, 126217, 162401	Plantilla:OEIS2
2	4, 6, 8, 10, 12, 14, 22, 24, 26, 30, 34, 38, 46, 56, 58, 62, 74, 82, 86, 94	Plantilla:OEIS2
3	9, 15, 21, 33, 39, 51, 57, 63, 69, 87, 93	Plantilla:OEIS2
4	6, 8, 12, 16, 20, 24, 28, 40, 44, 48, 52, 60, 68, 76, 80, 92	Plantilla:OEIS2
5	25, 65, 85, 145, 165, 185, 205, 265, 305, 365, 445, 485, 505, 545, 565, 685, 745, 785, 825, 865, 905, 965, 985	Plantilla:OEIS2
6	8, 10, 12, 18, 24, 30, 36, 42, 66, 72, 78, 84, 90
7	9, 15, 49, 91, 133, 217, 259, 301, 427, 469, 511, 553, 679, 721, 763, 889, 973
8	10, 12, 14, 16, 20, 24, 32, 40, 48, 56, 60, 80, 88, 96
9	21, 27, 45, 63, 99, 105, 117, 153, 171, 189, 207, 261, 273, 279, 333, 369, 387, 423, 429, 477, 513, 531, 549, 585, 603, 639, 657, 711, 747, 801, 873, 909, 927, 945, 963, 981
10	12, 24, 28, 30, 50, 70, 110, 130, 150, 170, 190, 230, 290, 310, 330, 370, 410, 430, 442, 470, 530, 532, 550, 590, 610, 670, 710, 730, 790, 830, 890, 910, 970
11	15, 35, 121, 341, 451, 455, 671, 781
12	14, 16, 18, 20, 22, 24, 36, 40, 42, 48, 60, 72, 80, 84
13	14, 15, 33, 169, 481, 793, 805, 949
14	15, 16, 18, 24, 26, 30, 44, 56, 98, 182, 264, 266, 392, 434, 510, 518, 602, 854, 938
15	16, 21, 39, 55, 63, 75, 195, 255, 275, 315, 435, 495, 555, 615, 795, 819, 915, 975
16	18, 20, 24, 28, 32, 40, 48, 52, 60, 64, 66, 80, 96
17	65, 77, 289, 665, 1649, 1921
18	20, 24, 30, 34, 36, 42, 54, 72, 78, 84, 88, 90
19	21, 51, 91, 361, 595, 703, 1387, 1955
20	22, 24, 38, 40, 48, 56, 60, 68, 80, 100
21	45, 57, 63, 85, 105, 117, 147, 231, 273, 357, 399, 441, 483, 585, 609, 651, 741, 777, 861, 903, 987
22	24, 28, 30, 70, 76, 102, 130, 132, 242, 682, 902, 910
23	25, 33, 35, 95, 119, 143, 455, 529
24	26, 30, 32, 36, 40, 42, 44, 46, 48, 60, 72, 80, 84, 96
25	27, 69, 125, 133, 165, 325, 385, 425, 725, 825, 925

Referències

En anglés:

• Makowski, A. "Generalization of Morrow's D-Numbers." Simon Stevin 36, (1963): 71
• Ribenboim, P. The New Book of Prime Number Records. New York: Springer-Verlag (1989): 101
• Knödel Numbers en MathWorld.