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

Author

Amiram Eldar, Apr 01 2017

Keywords

• nonn
• fini
• full

Comments

Subsequence of A001422.

David Wells noted that 23 is the largest integer that is not the sum of distinct powers.

Examples

			22 is not in the sequence since 22 = 1 + 2^2 + 2^3 + 3^2.
		

References

• David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin 1987, p. 101.

Crossrefs

Cf. A001422, A001597.

Programs

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]]