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Search: id:A077816
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| A077816 |
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Wieferich numbers: n such that 2^phi(n) == 1 modulo n^2. |
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4
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| 1093, 3279, 3511, 7651, 10533, 14209, 17555, 22953, 31599, 42627, 45643, 52665, 68859, 94797, 99463, 127881, 136929, 157995, 228215, 298389, 410787, 473985, 684645, 895167, 1232361, 2053935, 2685501, 3697083, 3837523, 6161805, 11512569
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OFFSET
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1,1
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COMMENT
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A077815(a(n))=1;
The only known primes are a(1)=A001220(1)=1093 and a(3)=A001220(2)=3511, the Wieferich primes.
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REFERENCES
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R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see p. 28.
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LINKS
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RICHARD CRANDALL, KARL DILCHER and CARL POMERANCE, A SEARCH FOR WIEFERICH AND WILSON PRIMES, Mathematics of Computation, Volume 66, 1997.
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EXAMPLE
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A077815(3279) = 2^phi(3279) mod 3279*3279 = 2^phi(3*1093) mod 10751841 = 2^(3279*(1-1/3)*(1-1/1093)) mod 10751841 = 2^2184 mod 10751841 = 1, therefore 3279 is a term
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CROSSREFS
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Cf. A001220.
Sequence in context: A138698 A023698 A038469 this_sequence A001220 A115192 A091674
Adjacent sequences: A077813 A077814 A077815 this_sequence A077817 A077818 A077819
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Nov 17 2002
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 05 2005
More terms from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Jun 18 2005
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