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Date: 16-12-2020
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Date: 25-1-2021
882
Date: 20-4-2020
1565
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For every , let be the set of composite numbers such that if , (where GCD is the greatest common divisor), then .
Special cases include , which is the set of Carmichael numbers, and , which gives the D-numbers.
Makowski (1962/1963) proved that there are infinitely many members of for . The following table summarized Knödel numbers for small .
OEIS | ||
1 | A002997 | 561, 1105, 1729, 2465, 2821, 6601, 8911, ... |
2 | A050990 | 4, 6, 8, 10, 12, 14, 22, 24, 26, 30, ... |
3 | A033553 | 9, 15, 21, 33, 39, 51, 57, 63, 69, 87, ... |
4 | A050992 | 6, 8, 12, 16, 20, 24, 28, 40, 44, 48, ... |
5 | A050993 | 25, 65, 85, 145, 165, 185, 205, ... |
REFERENCES:
Makowski, A. "Generalization of Morrow's -Numbers." Simon Stevin 36, 71, 1962/1963.
Ribenboim, P. The New Book of Prime Number Records. New York: Springer-Verlag, pp. 125-126, 1989.
Sloane, N. J. A. Sequences A002997/M5462, A033553, A050990, A050992, and A050993 in "The On-Line Encyclopedia of Integer Sequences."
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