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A359930
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The number of practical numbers strictly between A005153(n) and A005153(n)^(1+1/n).
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1
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0, 0, 1, 1, 1, 2, 2, 2, 1, 3, 3, 2, 2, 2, 2, 1, 3, 4, 3, 3, 3, 2, 3, 4, 3, 3, 3, 3, 4, 3, 3, 2, 3, 3, 4, 3, 3, 3, 4, 4, 4, 4, 3, 2, 3, 4, 6, 6, 6, 5, 5, 5, 4, 4, 4, 3, 2, 3, 3, 6, 6, 5, 5, 5, 4, 4, 4, 6, 5, 6, 5, 5, 4, 4, 5, 5, 5, 5, 5, 4, 4, 4, 5, 5, 5, 6
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OFFSET
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1,6
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COMMENTS
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This sequence is based on Sun's conjecture that A005153(n)^(1/n) is a strictly decreasing sequence for n >= 3. This conjecture states for practical numbers what Firoozbakht's conjecture says for prime numbers, and implies that a(n) > 0 for n >= 3. It is valid at least for n <= 9991. The corresponding sequence for primes is A182134.
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LINKS
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EXAMPLE
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The tenth practical number, A005153(10), is 24. 24^(1+1/10) is approximately 32.98. There are 3 practical numbers between 24 and 32.98, namely 28, 30, and 32. Thus a(10) = 3.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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