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A225101
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Numerator of (2^n - 2)/n.
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4
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0, 1, 2, 7, 6, 31, 18, 127, 170, 511, 186, 2047, 630, 8191, 10922, 32767, 7710, 131071, 27594, 524287, 699050, 2097151, 364722, 8388607, 6710886, 33554431, 44739242, 19173961, 18512790, 536870911, 69273666, 2147483647, 2863311530, 8589934591, 34359738366, 34359738367, 3714566310
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OFFSET
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1,3
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COMMENTS
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That (2^n - 2)/n is an integer when n is prime can easily be proved as a simple consequence of Fermat's little theorem.
It was believed long ago that (2^n - 2)/n is an integer only when n = 1 or a prime. In 1819, Frédéric Sarrus found the smallest counterexample, 341; these pseudoprimes are now sometimes called "Sarrus numbers" (A001567).
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REFERENCES
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Alkiviadis G. Akritas, Elements of Computer Algebra With Application. New York: John Wiley & Sons (1989): 66.
George P. Loweke, The Lore of Prime Numbers. New York: Vantage Press, 1982, p. 22.
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LINKS
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EXAMPLE
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a(4) = 7 because (2^4 - 2)/4 = 7/2.
a(5) = 6 because (2^5 - 2)/5 = 6.
a(6) = 31 because (2^6 - 2)/6 = 31/3.
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MAPLE
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MATHEMATICA
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Table[Numerator[(2^n - 2)/n], {n, 50}]
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PROG
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(PARI) vector(100, n, numerator((2^n - 2)/n)) \\ Colin Barker, Nov 09 2014
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CROSSREFS
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KEYWORD
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easy,nonn,frac
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AUTHOR
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STATUS
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approved
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