Número de Knödel

Dado un número natural n, un número de Knödel es un número compuesto m con la propiedad de que cada i < m coprimo con m satisface $i^{m - n} \equiv 1 \pmod{m}$.

El conjunto de todos los números naturales dado n se denomina el conjunto de los números de Knödel K_n. Nótese que K₁ son los números de Carmichael.

Estos son los primeros números de Knödel K_n para 0 < n < 26.:^[1]

n	Kn	OEIS
1	561, 1105, 1729, 2465, 2821, 6601, 8911, 10585, 15841, 29341, 41041, 46657, 52633, 62745, 63973, 75361, 101101, 115921, 126217, 162401	A002997
2	4, 6, 8, 10, 12, 14, 22, 24, 26, 30, 34, 38, 46, 56, 58, 62, 74, 82, 86, 94	A050990
3	9, 15, 21, 33, 39, 51, 57, 63, 69, 87, 93	A033553
4	6, 8, 12, 16, 20, 24, 28, 40, 44, 48, 52, 60, 68, 76, 80, 92	A050992
5	25, 65, 85, 145, 165, 185, 205, 265, 305, 365, 445, 485, 505, 545, 565, 685, 745, 785, 825, 865, 905, 965, 985	A050993
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

Referencias

1. ↑ Table of small Knödel numbers

En inglés:

• 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
• Weisstein, Eric W. "Knödel Numbers." From MathWorld--A Wolfram Web Resource. [1]