OFFSET
1,2
COMMENTS
There is a proof by Schinzel and Sierpinski that if n >= 33^17 + 12, then n can be written as a sum of four proper powers. Paul Pollack and Enrique Treviño improved that result to find the complete list.
REFERENCES
Paul Pollack & Enrique Treviño, Sums of Proper Powers, The American Mathematical Monthly, 128 (2021), no. 1, p. 40.
A. Schinzel and W. Sierpinski, Sur les puissances propres, Bull. Soc. Roy. Sci. Liege, 34 (1965), pp. 550-554.
EXAMPLE
The first few missing terms are
16 = 2^2 + 2^2 + 2^2 + 2^2,
20 = 2^2 + 2^2 + 2^2 + 2^3,
21 = 2^2 + 2^2 + 2^2 + 3^2,
24 = 2^2 + 2^2 + 2^3 + 2^3,
25 = 2^2 + 2^2 + 2^3 + 3^2,
26 = 2^2 + 2^2 + 3^2 + 3^2,
28 = 2^2 + 2^3 + 2^3 + 2^3.
CROSSREFS
KEYWORD
nonn,fini,full
AUTHOR
Enrique Treviño, Jan 03 2020
STATUS
approved