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A238194
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Conjectured numbers n for which n^n + (-1)^n (n-1)^(n-1) is not squarefree.
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2
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130, 257, 487, 528, 815, 897, 1176, 1225, 1320, 1373, 1430, 2029, 2050, 2084, 2198, 2247, 2526, 2608, 2895, 2936, 2958, 3166, 3679, 3849, 3909, 3950, 4237, 4319, 4598, 4647, 4723, 4795, 5472, 5487, 5620, 5669, 5948, 6030, 6317, 6358, 6588, 6677, 6936, 7101
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OFFSET
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1,1
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COMMENTS
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The first case (130) yields a number divisible by 83^2. The next 5 terms yield numbers divisible by 59^2. Boyd et al. are not completely certain about the other 994 numbers up to 1000. They conjecture that 0.9934466... of numbers n^n + (-1)^n (n-1)^(n-1) are squarefree.
Boyd et al. tested the values n <= 1000 for divisibility by the squares of the first 10^4 primes. To extend the sequence, I tested the divisibility of n <= 200000 by the squares of the first 10^5 primes. - Giovanni Resta, Feb 24 2014
The heuristic chance that Resta's list is incomplete is just over 1%. This drops to 0.07% with testing to the millionth prime. - Charles R Greathouse IV, Feb 25 2014
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LINKS
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PROG
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CROSSREFS
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Cf. A086797 (n^n + (-1)^n (n-1)^(n-1) with signs).
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KEYWORD
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nonn,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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