A284743 Positive numbers that are not the sum of (any number of) distinct perfect powers (A001597).

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.

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