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 A284743 Positive numbers that are not the sum of (any number of) distinct perfect powers (A001597). 0
 2, 3, 6, 7, 11, 15, 19, 23 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Subsequence of A001422. David Wells noted that 23 is the largest integer that is not the sum of distinct powers. REFERENCES David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin 1987, p. 101. LINKS Table of n, a(n) for n=1..8. EXAMPLE 22 is not in the sequence since 22 = 1 + 2^2 + 2^3 + 3^2. MATHEMATICA 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]] CROSSREFS Cf. A001422, A001597. Sequence in context: A308733 A363046 A049196 * A256976 A179019 A096578 Adjacent sequences: A284740 A284741 A284742 * A284744 A284745 A284746 KEYWORD nonn,fini,full AUTHOR Amiram Eldar, Apr 01 2017 STATUS approved

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Last modified August 6 00:03 EDT 2024. Contains 374957 sequences. (Running on oeis4.)