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A364637
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a(n) is the least k > 1 that can be represented as a sum of one or more distinct positive m-th powers for 1 <= m <= n.
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4
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OFFSET
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1,1
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COMMENTS
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Sprague showed that for any m, all sufficiently large integers are the sum of distinct m-th powers. A001661(m) gives the largest number not of this form, so we can use A001661 to write an upper bound for the terms here.
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LINKS
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FORMULA
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For n >= 2, a(n) <= 1 + Max_{m=2..n} A001661(m).
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EXAMPLE
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a(5) = 7809 as it can be written as a sum of one or more distinct positive m-th powers for 1 <= m <= 5 as follows. 1^5 + 2^5 + 6^5 = 2^4 + 6^4 + 7^4 + 8^4 = 3^3 + 5^3 + 14^3 + 17^3 = 1^2 + 8^2 + 88^2 = 7809^1 and no number less than 7809 can be written as such.
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CROSSREFS
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KEYWORD
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nonn,more,hard
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AUTHOR
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STATUS
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approved
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