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Search: id:A119534
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| A119534 |
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Largest prime divisor of numerator of the n-th Artin's product. |
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+0
3
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| 5, 19, 41, 109, 109, 271, 271, 271, 811, 929, 929, 929, 929, 2161, 2161, 2161, 3659, 4421, 4969, 4969, 4969, 4969, 4969, 9311, 10099, 10099, 10099, 10099, 10099, 16001, 17029, 17029, 19181, 22051, 22051, 22051, 22051, 22051, 22051, 22051, 32579
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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Artin's constant (A005596) is equal to Product[1-1/(Prime[k]*(Prime[k]-1)),{k,1,Infinity}]. n-th Artin's product is Product[1-1/(Prime[k]*(Prime[k]-1)),{k,1,n}]. a(n) is prime from A091568 of the form p^2-p-1, where p is prime from A091567.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics. Artin's Constant.
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FORMULA
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a(n) = Max[FactorInteger[Numerator[Product[1-1/(Prime[k]*(Prime[k]-1)),{k,1,n}]]]].
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MATHEMATICA
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Table[Max[FactorInteger[Numerator[Product[1-1/(Prime[k]*(Prime[k]-1)), {k, 1, n}]]]], {n, 2, 100}]
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CROSSREFS
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Cf. A091568, A091567, A005596, A048296.
Adjacent sequences: A119531 A119532 A119533 this_sequence A119535 A119536 A119537
Sequence in context: A125202 A024841 A100572 this_sequence A033622 A091568 A089148
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KEYWORD
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frac,nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 27 2006
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