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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
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.
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
Sequence in context: A308733 A363046 A049196 * A256976 A179019 A096578
KEYWORD
nonn,fini,full
AUTHOR
Amiram Eldar, Apr 01 2017
STATUS
approved