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A064080
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Zsigmondy numbers for a = 4, b = 1: Zs(n, 4, 1) is the greatest divisor of 4^n - 1^n (A024036) that is relatively prime to 4^m - 1^m for all positive integers m < n.
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5
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3, 5, 7, 17, 341, 13, 5461, 257, 1387, 41, 1398101, 241, 22369621, 3277, 49981, 65537, 5726623061, 4033, 91625968981, 61681, 1826203, 838861, 23456248059221, 65281, 1100586419201, 13421773, 22906579627, 15790321, 96076792050570581
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| By Zsigmondy's theorem, the n-th Zsigmondy number for bases a and b is not 1 except in the three cases (1) a = 2, b = 1, n = 1, (2) a = 2, b = 1, n = 6, (3) n = 2 and a+b is a power of 2.
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REFERENCES
| K. Zsigmondy, Zur Theorie der Potenzreste, Monatshefte fuer Mathematik und Physik 3 (1882), 265 - 284
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LINKS
| K. Zsigmondy, Zur Theorie der Potenzreste, Monatsh. f. Math. 3 (1892) 265-284.
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CROSSREFS
| Cf. A024036, A064078, A064079, A064081, A064082, A064083.
Sequence in context: A038893 A191064 A075227 * A184875 A112986 A052333
Adjacent sequences: A064077 A064078 A064079 * A064081 A064082 A064083
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KEYWORD
| nonn
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AUTHOR
| Jens Voss (jens.voss(AT)poet.de), Sep 04 2001
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EXTENSIONS
| Corrected and extended by Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 05 2001
Definition corrected by Jerry Metzger, Nov 04 2009
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