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 .
El conjunto de todos los números naturales dado n se denomina el conjunto de los números de Knödel Kn. Nótese que K1 son los números de Carmichael.
Ejemplos
Estos son los primeros números de Knödel Kn para 0 < n < 26.:Table of small Knödel numbers
n Kn OEIS 1 561, 1105, 1729, 2465, 2821, 6601, 8911, 10585, 15841, 29341, 41041, 46657, 52633, 62745, 63973, 75361, 101101, 115921, 126217, 162401 2 4, 6, 8, 10, 12, 14, 22, 24, 26, 30, 34, 38, 46, 56, 58, 62, 74, 82, 86, 94 3 9, 15, 21, 33, 39, 51, 57, 63, 69, 87, 93 4 6, 8, 12, 16, 20, 24, 28, 40, 44, 48, 52, 60, 68, 76, 80, 92 5 25, 65, 85, 145, 165, 185, 205, 265, 305, 365, 445, 485, 505, 545, 565, 685, 745, 785, 825, 865, 905, 965, 985 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
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
Enlaces externos
Knodel Knödel