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A284743 Numbers that are not the sum 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 (Numbers which are not the sum of distinct squares).

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: A018468 A117115 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 May 26 09:12 EDT 2017. Contains 287093 sequences.