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A284743
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Positive numbers that are not the sum of (any number of) distinct perfect powers (A001597).
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0
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OFFSET
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1,1
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COMMENTS
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David Wells noted that 23 is the largest integer that is not the sum of distinct powers.
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REFERENCES
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David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin 1987, p. 101.
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LINKS
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EXAMPLE
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22 is not in the sequence since 22 = 1 + 2^2 + 2^3 + 3^2.
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MATHEMATICA
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PerfectPowerQ[n_] := n==1 || GCD@@FactorInteger[n][[All, 2]]>1; a=Select[Range[128], PerfectPowerQ[#] &]; nn = Dimensions[a][[1]]; t=Rest[CoefficientList[Series[Product[(1 + x^a[[k]]), {k, nn}], {x, 0, a[[nn]]}], x]]; Flatten[Position[t, 0]]
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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STATUS
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approved
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