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%I #23 Aug 18 2017 14:31:49
%S 2,3,6,7,11,15,19,23
%N Positive numbers that are not the sum of (any number of) distinct perfect powers (A001597).
%C Subsequence of A001422.
%C David Wells noted that 23 is the largest integer that is not the sum of distinct powers.
%D David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin 1987, p. 101.
%e 22 is not in the sequence since 22 = 1 + 2^2 + 2^3 + 3^2.
%t 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]]
%Y Cf. A001422, A001597.
%K nonn,fini,full
%O 1,1
%A _Amiram Eldar_, Apr 01 2017
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